Enunciados Problemas 1516 Pepcan v01

February 23, 2023 | Author: Anonymous | Category: N/A

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Ofpcrtcgfnth of @nifn`frçc of R`stfgcs y Cuthgãt`bc

JVNOCGFN_HR Bursh ;=36-3:. OF CV_HGÃ_@BC Fnunb`cohs of prãbt`bcs of cudc y prhkdfgcs co`b`hncdfs. Fnunb`cohs of fxãgfnfs.

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fefgpdh Fef gpdh s of gh ghofdcoh. ofdcoh.

3. 3.  Cdturc of dçquòh bhntfnòh fn un ofpòs`th. Fd s`stfgc of dc jìurc fs un ofpòs`th of cdgcbfncg`fnth of dçquòh, quf rfb`kf jduòh, of ofnsòco bhnstcntf, phr dc pcrtf supfr`hr y dh fxtrcf gfo`cntf unc bhnoubb`òn gãs unc vãdvudc s`tucoc fn su kcsf. Zcr`ckdfs Zc r`ckdfs ofd g ghofdh5 hofdh5   



Z vhdugfn dçquòh fd ofpòs`th g gcsc of of dçquòh fn fn fd ofpòs`th  o fnsòco (quf sf bhnsòfrc bhnstcn bhnstcntf) tf)  J bcuocd vhdugàtr`bh of scdòc  q bcuocd vhdugàtr`b vhdugàtr`bh h of fntrcoc  u cpfrturc of dc vãdvudc of scdòc  a cdturc of dçquòh fn fd ofpòs`th ]crãgftrhs ]c rãgftrhs ofd ghofdh5 ghofdh5    C sfbb`òn ofd tcnquf (sf bhnsòfrc of sfbb`òn btf)  l pcrãgftrh of dc vãdvudc ]r`nb`p`hs jçs`bhs5 jçs`bhs5  Bhnsfrvcb`òn of dc gcsc  Fbucb`òn of Kfrnu`dd` cpd`bcoc c unc bhnoubb`òn + vãdvudc s`n pàroòcs.

;. R`stfgc Fdfbtrhgfbãn`bh. Bhntrhd of phs`b`òn fn dczh ck`frth of unc gcsc c pcrt`r of dc tfns`òn of cd`gfntcb`òn u(t). Dc jufrzc J (t) (t) ifnfrcoc phr fd shdfnhòf fs prhphrb`hncd c dc `ntfnsòco quf b`rbudc phr dc khk`nc.

2. unc rfs`stfnb`c (Ofpòs`th bhn bhntrhddcof tfgpfrcturc). Fd _cnquf s`stfgc bhn of dc jìurc t`fnf phr hkefth gcntfnfr tfgpfrcturc _ ofd ciuc bhntfnòc (y quf scdf) fn fd ofpòs`th, uscnoh pcrc fddh un s`stfgc of bcdfjcbb`òn fdàbtr`bc (sf gcn`pudc dc tfns`òn of cd`gfntcb`òn Z). Cd ofpòs`th df ddfic un bcuocd of dçquòh dçquòh vcr`ckdf, q, c unc tfgpfrcturc bhns bhnstcntf tcntf _`. Fnbufntrf fd ghofdh gctfgãt`bh quf rfdcb`hnc fd bcuocd q(t) y fd vhdtcef Z(t) bhn dc tfgpfrcturc fn fd ofpòs`th _(t).

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

?. ?. A cddcr fd ghofdh gctfgãt`bh ofd s`stfgc of dc jìurc bhnsòfrcnoh bhgh scdòc dc phs`b`òn ofd fef of dc gfsc gfsc i`rcthr`c y fntrcoc dc tfns`òn o of f cd`gfntcb`òn

D`nfcd`zcb`òn.

6. 6. F xcgfn fxtrchro`ncr`h 33-3; (prhkdfgc, cpcrtcoh 3) Vn surtòhr of icshd`nc pufof ghofdcrsf gfo`cntf dc fbucb`òn ;

oS (t )

 u(t )  ?S ; (t )  S(t ) ,

ot

ohnof S(t) fs fd bcuocd of icshd`nc quf oc fd surtòhr (d`trhs/sfiunoh) y u(t) fs dc tfns`òn of fntrcoc cd ghthr of dc khgkc ofd surtòhr (vhdt`hs), quf sf pufof gcn`pudcr c vhduntco. D`nfcd`zcr fsc fbucb`òn s` fd punth of trckceh fdfiòh fs of S7=. d`trhs/sfiunoh. :. :.  Fxcgfn hro`ncr`h 33-3; (prhkdfgc, cpcrtcohs 3 y ;) Rfc un prhbfsh of bcdfntcg`fnth of un jduòh. Fd jduòh ddfic cd o`sphs`t`vh bcdfjcbthr c unc tfgpfrcturc _` (µB), quf pufof vcr`cr bhn fd t`fgph, t` fgph, y ofspuàs ofd prhbfsh of bcdfntcg`fnth scdf bhn unc tfgpfrcturc _ (µB). (µ B). Rf o`sphnf of unc vãdvudc of rfiudcb`òn quf pufof gho`j`bcr fd bcuocd of dçquòh (q) quf b`rbudc phr fd o`sphs`t`vh bcdfjcbthr. Rf ofnhg`nc u (%) c dc cpfrturc of o`bac vãdvudc. Fd ghofdh gctfgãt`bh quf pfrg`tf bcdbudcr dc fvhdub`òn of dc tfgpfrcturc of scdòc ofd jduòh fn junb`òn of dc tfgpfrcturc of fntrcoc y of dc cpfrturc of dc vãdvudc of rfiudcb`òn fs5 2

o_ (t ) ot

 :_ (t )  1.1u ; (t )  ;_ ` (t )

Bucnoh fd s`stfgc fstã fn fstcoh fstcb`hncr`h y dc tfgpfrcturc of fntrcoc fs of 3= µB, dc of scdòc fs of ?=µB. Rf pòf5 3) @ofnt`j`bc dcs vcr`ckdf vcr`ckdfss ofd prhkdfgc, buc bucdd fs dc fntrcoc, buc bucdd fs dc scdòc y buãd fs dc pfrturkcb`òn. ;) Bhn dc fbucb fbucb`òn `òn o`jfrfnb`cd ococ c cntfr`hrgfntf ntfr`hrgfntf bcdbudc dc junb`òn of trcnsjfrf trcnsjfrfnb`c nb`c of dc scdòc rfspfbth of dc fntrcoc y dc junb`òn of trcnsjfrfnb`c of dc scdòc rfspfbth of dc pfrturkcb`òn. O`kuec fd o`circgc of kdhqufs ofd s`stfgc bhnsòfrcoh bhn sus junb`hnfs of trcnsjfrfnb`c.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

2

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

9. 9. D `nfcd`zcr fd s`stfgc rfprfsfntcoh r fprfsfntcoh phr dcs fbucb`hnfs5

o ; x ot ; y

;



6 oy ot

ox ot

u  u ; y

;

 6 x  u

Fn thrnh cd punth u= 73 73, bhnsòfrcnoh thocs dcs ofr`vcocs nudcs fn fstf punth. 1. D`nfcd`zcr dc sìu`fntf fbucb`òn fn thrnh cd punth x =73 y suphn`fnoh ofr`vcocs nudcs. R` x pcsc krusbcgfntf c vcdfr 3.6, bhgpcrcr dc o`jfrfnb`c fntrf fd ghofdh d`nfcd y fd rfcd ofd vcdhr  3 j`ncd of dc scdòc. x y  ; y x  sfn(  y )  bhs xsfn  :

;

0. 0. _ cnquf bhn s`stfgc of bcdfjcbb`òn (fbucb`hnfs v`stcs fn ghofdcoh)

Fn fd tfgc of ghofdcoh sf ac hktfnòh bhgh fbucb`òn Z o

o _ (t ) o t

 q(t )¹ )¹((_ `  _ (t )) 

Z (t )

;

 ¹bf¹ [

Ruphn`fnoh quf _`7;=µB, [73==K, q=7 ;=, Z=73;=, 73, Bf73, a73, C7;  Bcdbudcr fd punth of d`nfcd`zcb`òn  Ghofdh d`nfcd.  [fprfsfntcb`òn fn fspcb`h of fstcohs (hpb`hncd). 3=. ]crc fd s`stfgc fdfbtrhgfbãn`bh of dc jìurc buyh ghofdh (d`nfcd) yc sf ac fstuo`coh, 3=. hktfnfr su rfprfsfntcb`òn fn fspcb`h of fstcohs (hpb`hncd). u(t )  [¹`3 (t )  Z b (t ) oZ b (t ) 3  `3 (t )  `; (t )  ot B o` Z b (t )  D¹ ; (t ) ot g¹

o ; x(t ) ;

 J (t )  L ¹ x (t )  k¹

ot J ( t )   ¹`; ( t )

ox(t ) ot

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

?

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

_rcnsjh _rc nsjh rgcoc of Dcpdcbf. J Junb` unb` òn of _rcnsjfrf _rcnsjfrfnb`c. nb`c. O`c O`circgcs ircgcs of k kdhqu dhqu fs.

33. Fxcgfn fxtrchro`ncr`h 33 33-3; -3; (Cpcrtcoh 3). Rf bhnstruyf un s`stfgc of bhntrhd pcrc rfiudcr fd vhdugfn of icshd`nc sug`n`strcoc, Z(t). ]crc fddh sf pdcntfc fd s`stfgc of bhntrhd of dc jìurc. Fn o`bah fsqufgc fd vhdugfn of d`trhs ofsfcohs fs Zrfj . Rf sckf quf dc rfdcb`òn fntrf fd vhdugfn y fd bcuocd of icshd`nc sug`n`strcoh phr fd surtòhr oZ (t ) v`fnf ocoh phr dc sìu`fntf fbucb`òn o`jfrfnb`cd ot  S (t ) . Fdfiòh fd punth of trckceh S7=. d`trhs/sfiunoh, bcdbudf dc junb`òn of trcnsjfrfnb`c quf rfdcb`hnc fd vhdugfn of icshd`nc sug`n`strcoh phr fd surtòhr bhn dc tfns`òn of cd`gfntcb`òn of dc khgkc ofd surtòhr (I(s) fn dc jìurc).

3;. Fxcgfn hro`ncr`h 33-3; (prhkdfgc, cpcrtcohs 3 y ;) Rfc un prhbfsh of bcdfntcg`fnth of un jduòh. Fd jduòh ddfic cd o`sphs`t`vh bcdfjcbthr c unc tfgpfrcturc _` (µB), quf pufof vcr`cr bhn fd t` t`fgph, fgph, y ofspuàs ofd prhbfsh of bcdfntcg`fnth scdf bhn unc tfgpfrcturc _ (µB). (µ B). Rf o`sphnf of unc vãdvudc of rfiudcb`òn quf pufof gho`j`bcr fd bcuocd of dçquòh (q) quf b`rbudc phr fd o`sphs`t`vh bcdfjcbthr. Rf ofnhg`nc u (%) c dc cpfrturc of o`bac vãdvudc. Fd ghofdh gctfgãt`bh quf pfrg`tf bcdbudcr dc fvhdub`òn of dc tfgpfrcturc of scdòc ofd jduòh fn junb`òn of dc tfgpfrcturc of fntrcoc y of dc cpfrturc of dc vãdvudc of rfiudcb`òn fs5 2

o_ (t ) ot

 : _ (t )  1.1u ; (t )  ;_ ` (t ) . Bucnoh fd s`stfgc fstã fn fstcoh fstcb`hncr`h y dc

tfgpfrcturc of fntrcoc fs of 3= µB, dc of scdòc fs of ?=µB. Rf pòf5 3) @ofnt`j`bc dcs vcr`ckdf vcr`ckdfs s ofd prhkdfgc, buc bucdd fs dc fntrcoc, bu bucd cd fs dc scdòc y buãd fs dc pfrturkcb`òn. ;) Bhn dc fbucb fbucb`òn `òn o`jfrfnb`cd ococ cntfr`hrgfntf bcdbudc dc junb`òn of trcnsjfrf trcnsjfrfnb`c nb`c of dc scdòc rfspfbth of dc fntrcoc y dc junb`òn of trcnsjfrfnb`c of dc scdòc rfspfbth of dc pfrturkcb`òn. O`kuec fd o`circgc of kdhqufs ofd s`stfgc bhnsòfrcoh bhn sus junb`hnfs of trcnsjfrfnb`c. ;

o x  6 ox u  u ; y  ; ; ot ot oy ;  6 x  u y  ot Fn thrnh cd punth u= 73, 73, bhnsòfrcnoh thocs dcs ofr`vcocs nudcs fn fstf punth (yc v`sth). Suà vcdhrfs sf hkt`fnfn s` u pcsc c vcdfr 3.3 (bhgpcrcr rfsudtcohs ofd ghofdh d`nfcd bhn fd nh d`nfcd)

32. D`nfcd`zcr fd s`stfgc rfprfsfntcoh phr dcs fbucb`hnfs5

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

6

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

3?. Fxcgfn hro`ncr`h 3;-32 (bufst`òn 3) Ocoh fd o`circgc of kdhqufs of dc jìurc5 Rf pòf5 c) Fxprfscrdh fn dc jhrgc

; s   k) R`5 A 3 s   ;, A ; s   3, I3 s   3, I

2s  ? s 3

, I2 s   2, I? s  

3 s

bcdbudcr I(s), A(s) y Dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh b) Bhnsòfrcnoh dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh ofd cpcrtcoh k), ¸Buãd sfrçc fd t`fgph of fstckdfb`g`fnth s` sf cpd`bcsf unc fntrcoc fsbcdòn un`tcr`h cd s`stfgc8, ¸Acy shkrfp`bh8 36. Fxcgfn hro`ncr`h 3;-32 (bufst`òn 2) Fd prhbfsh of dc jìurc rfprfsfntc un ahrnh of bcdfntcg`fnth of un gctfr`cd, quf fntrc c tfgpfrcturc _` y ofkf scd`r c tfgpfrcturc _. Fn fd ahrnh sf pufof gcn`pudcr fd jdueh J of fdfgfnth bcdfjcbthr pcrc acbfr quf dc tfgpfrcturc j`ncd _ ofd gctfr`cd cdbcnbf dhs vcdhrfs ofsfcohs. Rf sckf quf dc rfdcb`òn fntrf dc tfgpfrcturc _, dc tfgpfrcturc of fntrcoc ofd gctfr`cd _` y fd jdueh J v`fnf ococ phr5 o_ 6  2J   ;_   ;  2J_  _ ` ot bhn _ y _` fn µB, J fn Li/g`n y fd t`fgph fn g`nuths, y quf bucnoh fd s`stfgc fstã fn fstcoh fstcb`hncr`h c ?=µB dc tfgpfrcturc of fntrcoc fs of 3=µB. Hktfnfr ddc c junb`òn of trcnsjfrfnb`c ofd s`stfgc fn fsf punth of trckceh, y o`kuecr fd o`circgc of kdhqufs, òfnt`j`bcnoh dc vcr`ckdf of fntrcoc, dc vcr`ckdf of scdòc y dc pfrturkcb`òn. 3:. Fxcgfn fxtrchro`ncr`h 3;-32 (bufst`òn ;) Rfc un s`stfgc bhgh fd of dc jìurc, ohnof5 ;= V(s ) V(s) B(s) B(s ) I s   ; ; s  9 s  3; s  ;s  ; I Rf cpd`bc bhgh fntrcoc unc rcgpc un`tcr`c. Rf pòf5 c) Hktfnfr dc ofsbhgphs`b`òn fn jrcbb`hnfs s`gpdfs of dc scdòc ofd s`stfgc, sfócdcnoh y eust`j`bcnoh quà tàrg`nhs bhrrfsphnofn c dc rfspufstc trcns`thr`c y bucdfs c dc pfrgcnfntf. (Bhgfntcr`h5 nh fs nfbfscr`h acbfr dhs bãdbudhs nugàr`bhs) k) R` fd nugfrcohr of I(s) jufrc 6=, ¸sf vfrçc cjfbtcoh fd ofscrrhddh of cdiunc jhrgc8







39. ]crc fd ghthr of BB of dc jìurc acddcr dc J of _rcnsjfrfnb`c y fd o`circgc of kdhqufs. Fntrcoc f` (t ) t fns`òn cpd`bcoc. Rcdòc  g (t ) phs`b`òn ofd rhthr. ;

E

o  g (t ) ;

ot

 L   _  @ (t )  K¹

f` (t )  [@ (t )  D   o@ (t ) ot

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

o  g (t ) ot

 l k ¹ o  g (t ) ot

:

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

31. _ 31. cnquf bhn s`stfgc of bcdfntcg`fnth (fbucb`hnfs v`stcs fn ghofdcoh) Fn fd tfgc of ghofdcoh sf ac hktfnòh bhgh fbucb`òn5 Z o

o _ (t ) o t

 q(t )¹ )¹((_ `  _ (t )) 

Z (t );

 ¹bf¹ [

Ruphn`fnoh quf _`7;=µB, [73==K, q=7 ;=, Z=73;=, =.3 o _ (t )  _ (t )   =.2:¹ q(t )  =.3;¹ Z (t ) o t σ73, Bf73, a73, C7; y sf d`nfcd`zc, sf hkt`fnf5 Bcdbudcr su junb`òn of trcnsjfrfnb`c bhn bhno`b`hnfs `n`b`cdfs nudcs 30.  Fd s`stfgc fdfbtrhgfbãn`bh of dc jìurc yc sf fstuo`ò fn fd tfgc of ghofdcoh. 30. u (t )  [¹`3 (t )  Z b (t ) oZ b ( t ) ot g¹



o ; x(t ) ;

3 B

`3 (t )  `; (t ) 

Z b (t )  D¹

 J (t )  L ¹ x(t )  k¹

ot J (t )   ¹`; ( t )

ox(t ) ot

o`; ot

(t )

c) Hktfnfr dcs Junb`hnfs of _rcnsjfrfnb`c y dhs o`circgcs of kdhqufs bhrrfsphno`fntfs. k) C pcrt`r of dc rfprfsfntcb`òn fn fspcb`h of fstcohs quf sf gufstrc hktfnfr dc gctr`z of trcnsjfrfnb`c I(s) pcrc dc quf sf bugpdf quf Q(s)7I(s)V(s)( hpb`hncd). = =    =L 3k    x(t )   =   x(t )  =     v(t )  g g g   v (t )   =         3 3   ¹ Z b (t )   3 ¹u(t ) = Z b (t )  = B ¹ [ B     B ¹ [   ` (t )   3 `; (t )   =   ;   =  = =  D 

 x(t )   v(t )    =¹u(t ) x (t )  3 = = =¹  Z b (t )  ` (t )  ; 

;=. Junb`òn of trcnsjfrfnb`c y o`circgc of kdhqufs ofd ghthr. ;=. Acddcr dc Junb`òn of _rcnsjfrfnb`c ofd s`stfgc of dc jìurc bhns bhnsòfrcnoh òfrcnoh bhgh scdòc dc phs`b`òn ofd fef of dc gfsc i`rcthr`c y fntrcocs dc tfns`òn of cd`gfntcb`òn y fd pcr pfrturkcohr cbtucnoh shkrf dc gfsc. o  g (t ) f` (t )  L k ot   _ g (t  )  L _ ` (t )

o`(t )

 [r `(t )  Dr

;

E fq

o  g (t ) ot ;

 b ( t ) 

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

N 3 N ;

 _ g (t ) 

N 3 N ;

ot

_ o (t )  j fq

o  g (t ) ot

 g (t )

9

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

;3. Dc jìurc gufstrc un s`stfgc of dfv`tcb`òn gcinàt`bc ;3. Dc quf pfrg`tf tfnfr suspfnoòc fn fd c`rf unc fsjfrc gftãd`bc of gcsc g. Fd hkeft`vh ofd bhntrhdcohr sfrã rfiudcr fd vcdhr of dc bhrr`fntf ofd b`rbu`th ofd fdfbtrh`gãn, of tcd jhrgc quf dc fsjfrc sf gcntfnic c unc o`stcnb`c bhnstcntf x7Q ofd fdfbtrh`gãn. Dcs fbucb`hnfs quf rìfn fd bhgphrtcg`fnth shn5 D

g

o`(t )

  [`(t )  v (t )

ot ; o x(t ) ;

ot

;

 gi  j g (t )  gi 

b` (t ) x(t )

Dhs vcdhrfs of dhs pcrãgftrhs shn5 b73< i70.1< g7=.3< [73< D7=.=3< Q =7=.=1< Hktfnic dc junb`òn of trcnsjfrfnb`c ofd s`stfgc5

Q ( s ) Z ( s )

;;. ]crc dhs s`stfgcs of dcs jìurcs j ìurcs 3 y ; hktfnic dcs junb`hnfs of trcnsjfrfnb`c

B ( s )

]( s )

_hgf Ib(s)72=. Ib(s)72=. s 3

;s  3 [(s) +

Ib(s) -

+ V(s)

3

+

s 3

](s) +

+

s  =.6

;s ;  s  2

B(s)

Jìurc 3

Jìurc ;

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

1

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[fspufst [f spufst c tfgphrcd. R`st R`st fgcs fgcs of pr `gfr hr hrofn. ofn.

;2.   _c ;2. _cnquf nquf bhn s`stfgc s`s tfgc of bcdofh. bcdofh.   Fn fd tfgc of ghofdcoh sf ac hktfnòh bhgh fbucb`òn5 Z o

o _ (t ) o t

)¹ (_ `  _ (t ))   q(t )¹(

Z (t );

 ¹bf¹ [

Ruphn`fnoh quf _`7;=µB, [73==K, q=7 ;=, Z=73;=, σ73, Bf73, a73, C7; y sf d`nfcd`zc, sf hkt`fnf5 o _ (t )  _ (t )   =.2:¹q(t )  =.3;¹Z (t ) =.3 o t

 =.2:¹ =.3; P su junb`òn of trcnsjfrfnb`c t rcnsjfrfnb`c bhn bhno`b`hnfs _ ( s )  S ( s )  Z ( s ) `n`b`cdfs nudcs fs fnthnbfs =.3s  3 =.3s  3 Rf pòf5 - Bhgh fs dc rfspufstc ofd tcnquf cntf unc fntrcoc fs fsbcdòn bcdòn fn S(s) of gcin`tuo 3, y cntf unc fntrcoc fn `gpudsh y rcgpc. - Bhgpcrc dhs rfsudtcohs bhn Gctdck. - P cntf un fsbcdòn fn dc fntrcoc Z(s). - Bhgfntc dc fstck`dòco ofd s`stfgc fn thohs dhs bcshs. ;?.   B`rbu`th [B ;?. [B -

-

Acddcr fd vhdtcef fn dcs khrncs ofd bhnofnscohr ofd b`rbu`th quf sf gufstrc fn dc jìurc. Rupònicsf bhno`b`hnfs `n`b`cdfs nudcs (bhnofnscohr ofsbcricoh) y rfshdvfr cncdçt`bcgfntf y bhn Gctdck. Acddcr dc bh bhnstcntf nstcntf of t`fgph, dc icncnb`c y f fdd t`fgph t`fgph of of csfntcg`fnth of fstf s`stfgc bucnoh [73= y B7=.3 y acy un scdth fn fd phtfnb`cd of fntrcoc v(t) of gcin`tuo 6.

;6. _frgògftrh. _frgògftrh.   Vn tfrgògftrh sf fnbufntrc `n`b`cdgfntf fn fqu`d`kr`h fn un kcóh c tfgpfrcturc _ x (rfb`p`fntf x > ?=µ). Fd 3). Rf rft`rcrfqu`frf y sf sugfrif fn htrh kcóh (rfb`p`fntf ;) vcdhr c tfgpfrcturc of Ofspuàs ?= µB (_ of tfrgògftrh of ? g`nuths pcrc ddficr cd 01% ofd j`ncd gfoòh. cdbcnzcr dc tfgpfrcturc j`ncd, fd tfrgògftrh fs rf-`ntrhoubòh rãpòcgfntf fn fd kcóh 3. Cd bckh of ; g`nuths dc dfbturc ofd `nstrugfnth fs of := µB. Ruphn`fnoh quf fd tfrgògftrh fs un s`stfgc of pr`gfr hrofn, sf pòf5 - Dc bhnstcntf of t`fgph. - Dc tfgpfrcturc _x. - Dcs irãj`bc of _g fn fd t`fgph. _fgpfrcturc _fg pfrcturc fn fd kcóh5 _x



Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs ]rãbt`bcs ]rãbt`bcs Cudc

_fgpfrcturc _fg pfrcturc gfoòc5 _g

_fgpfrcturc fn fd kcóh5 ?=µB



0

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c. ;:.   Ofpòs`th ;:.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

]crt`fnoh ofd ghofdh nh d`nfcd C ghofdh d`nfcd`zcoh C -

o a (t )

ot

uh l



ot

oa(t )

 q(t )  u(t )l a(t ) sf ddfic c un

a(t )  q(t )  l

; ah

a=  u ( t )

Hktfnfr dcs jun junb`hnfs b`hnfs of trc trcnsjfrfnb`c nsjfrfnb`c quf rfdcb`hncn dc scdòc a bh bhn n dc dcss fntrcocs u,q. Hktfnfr dhs vc vcdhrfs dhrfs nugàr`bhs of f fscs scs J_ s` sf thgc fd pu punth nth of

-

=73 g, q=73= g2/a, l7=.;, C7; g;, u=76= fqu`d`kr`h5 agfo`cntf Bhgpcrcr, Gctdck, dc rf rfspufstc spufstc ofd s` s`stfgc stfgc cntf u un n scd scdth th of 3= fn dc fntrcoc V s` sf thgcn vcdhrfs ckshduths h dhs `nbrfgfnths. - Bhgpcrcr, gfo`cntf Gctdck, dc rf rfspufstc spufstc ofd s` s`stfgc stfgc cntf u un n scd scdth th of 2 fn dc fntrcoc S s` sf thgcn vcdhrfs ckshduths h dhs `nbrfgfnths. - Suà subfofrçc s` fd scdth fn fd bcuocd jufrc of 36 Zcr`ckdfs Zc r`ckdfs ofsv`cb`òn ofsv`cb`òn55 a 7 a ‒ a= q 7 q ‒ q= u 7 u ‒ u=. Vscnoh fscs vcr`ckdfs `nbrfgfnth5

-

A ( s ) 

L 3

 s  3

V ( s ) 

L ;

 s  3

S( s)

L 3  

ohnof

;a= u=

L ;   

; a= u= l

 

; C a= lu=

S(s) L ;

 s  3

+

V(s)

L 3

 s  3

A(s) Q

+

3. Rf pòf bcdbudcr dc rfspufstc tfgphrcd ofd n`vfd cntf un bcgk`h of t`ph scdth un`tcr`h fn dc cpfrturc of dc vãdvudc5 icncnb`c j`ncd, jhrgc of dc burvc… A ( s)  

=.=? =.? s  3

V  ( s ) 

=.; =.? s  3

S( s)

;. Bhgprhkcr, ut`d`zcnoh Gctdck, dc rfspufstc tfgphrcd ofd n`vfd cntf un bcgk`h of tt`ph `ph `gpudsh un`tcr`h, scdth un`tcr`h y rcgpc un`tcr`c - Fn dc cpfrturc of dc vãdvudc - Fn fd bcuocd of fntrcoc - ¸Buãd fs fd t`fgph of csfntcg`fnth8 2. Rf pòf rfpft`r dhs fxpfr`gfnths pcrc un ãrfc ofd ofpòs`th gcyhr5 C7? g;. ¸Suà sf pufof ofb`r shkrf dc vfdhbòco of rfspufstc8 ;9.F ;9. nbhntrcr dc junb`òn of trcnsjfrfnb`c ofd s`stfgc buyc scdòc cntf un fsbcdòn un`tcr`h fs fd of dc jìurc5 [fspufstc of un s`stfgc cntf un fsbcdòn un`tcr`h 6 ?.6 ? 2.6 2    o   u    t    `    d ;.6   p   g    C

;

3.6 3 =.6 =

=

;

?

:

1

3=

3;

3?

3:

31

;=

_`fgph (sfbhnos)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

3=

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[fspufst [f spufst c tfgphrcd. R`st R`st fgcs fgcs of sfiun sfiunoh oh h rofn.

;1.( Bufst`òn ;, fxcgfn fxtrchro`ncr`h 33-3;) ;1. ]crc fd s`stfgc of dc jìurc acddcr5 c) Fbucb`òn bcrcbtfrçst`bc. k) Zcdhr ofd pcrãgftrh —c‗ (c>= ) of jhrgc quf fd bhneunth tfnic cghrtìucg`fnth brçt`bh. b) R` L  sf jèc fn Lgcx , acddcr5 (3) [fspufstc fstcb`hncr`c ofd s`stfgc cntf un fsbcdòn unòco (bcsh of s`stfgc brçt`bcgfntf cghrtìucoh) y (;)t`fgph of fstckdfb`g`fnth.

;0. Fxcgfn hro`ncr`h 3;-32 (bufst`òn 3) Ocoh fd o`circgc of kdhqufs of dc jìurc5 Rf pòf5 c) Fxprfscrdh fn dc jhrgc

k) R`5

; s   A 3 s   ;, A ; s   3, I3 s   3, I

2s  ? s 3

, I2 s   2, I? s  

3

s (Z`sth fn _Dcpdcbf-J_rcnsjfrfnb`c) _Dcpdcbf-J_rcnsjfrfnb`c)

bcdbudcr I(s), A(s) y Dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh b) Bhnsòfrcnoh dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh ofd cpcrtcoh k), ¸Buãd sfrçc fd t`fgph of fstckdfb`g`fnth s` sf cpd`bcsf unc fntrcoc fsbcdòn un`tcr`h cd s`stfgc8, ¸Acy shkrfp`bh8 2=.- Oftfrg`ncr dc rfspufstc of un s`stfgc buyh ghofdh gctfgãt`bh v`fnf ocoh phr dc fbucb`òn o`jfrfnb`cd 



G  y (t )  K y ( t )  Ly (t )  r (t )

Bucnoh sf df shgftf c unc fntrcoc nudc y sf thgc bhgh bhno`b`hnfs `n`b`cdfs5. `n`b`cdfs5. y (=)  =.3   f y (=)  =.=6 s`fnoh5 G 73Li, 73Li, K72Ns/g y L 7;N/g 7;N/g 23.- ]crc fd s`stfgc ofd fefrb`b`h cntfr`hr, suphnic quf G, K y L   shn ofsbhnhbòhs, pfrh sf sckf quf su rfspufstc (fn g) cntf unc fntrcoc fsbcdòn un`tcr`h fs dc quf sf gufstrc fn dc jìurc. Fnbhntrcr dhs vcdhrfs of G, K y L .

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

33

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

2;. Ocoh fd s`stfgc of dc jìurc quf prfsfntc ohs kdhqufs ofsbhnhbòhs C y K bhn junb`hnfs of 2;. trcnsjfrfnb`c ofsbhnhbòcs, sf prftfnof hktfnfr dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh ofd s`stfgc idhkcd. C dhs s`stfgcs C y K sf dfs ac shgftòh c sfnocs fntrcocs fsbcdòn hktfn`ànohsf dcs rfspufstc quf sf `no`bcn fn dcs jìurcs jì.3 pcrc C y jì.; pcrc K.

22.  B`rbu`th [DB 22. ¸Bògh fs dc rfspufstc ofd b`rbu`th [DB cntf unc fntrcoc fsbcdòn un`tcr`h fn Z(s)8 Fstuo`cr su fstck`dòco. Bhgprhkcr fd rfsudtcoh bhn Gctdck Bcsh 3. [7;, D73 y B7=.=?. Bcsh ;. [73;, D73 y B7=.=?. 2?. R 2?. `stfgc gcsc-gufddf Bògh fs dc rfspufstc ofd s`stfgc cntf unc fntrcoc fsbcdòn un`tcr`h fn j(t). Bcsh 3. g73< k72< l7; Bcsh ;. g73, k73< l7=.;6 Bcsh 2. g73< k7;< l7; j (t )  g 

o ; x t   k  ox t   l  x t  ot ot

Q ( s ) 

3 J ( s ) gs  ks  l ;

26. [fcbthr quçg`bh. 26. ¸Buãd fs su junb`òn of trcnsjfrfnb`c, bucnoh cntf unc fntrcoc fn fsbcdòn fn dc cpfrturc of dc vãdvudc of vcphr u(t), of gcin`tuo 3=, tfnih fstc scdòc fn dc tfgpfrcturc _(t)8 Rtfp[fsphnsf

:=

6=

?=   f    o   u    t    `    d   p   g    C

2=

;=

3=

= =

;

?

:

1

3=

3;

_`gf(sfbhnos)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

3;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

2:. Bcgk`cohr of bcdhr 2:. ¸Buãd fs su junb`òn of trcnsjfrfnb`c, bucnoh cntf unc fntrcoc fn fsbcdòn fn u(t) of gcin`tuo 3=, sf hkt`fnf dc scdòc quf sf gufstrc fn dc tfgpfrcturc _(t)8

29. Fn un prhbfsh of sfbcoh sf `ntrhoubf cd sfbcofrh un b`frth gctfr`cd, eunth bhn unc bhrr`fntf 29. of c`rf bcd`fntf buyh bcuocd pufof gcn`pudcrsf phr gfo`h of dc sfócd of un s`stfgc vfnt`dcohr. Fstcnoh fn un punth of fqu`d`kr`h, sf rfcd`zc un fxpfr`gfnth bhns`stfntf fn o`sg`nu`r dc sfócd cd vfnt`dcohr un 3%, hksfrvãnohsf un bcgk`h fn dc augfoco ofd gctfr`cd bhgh fd ghstrcoh fn dc jìurc. Rf pòf bcdbudcr dc junb`òn of trcnsjfrfnb`c ofd sfbcofrh.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

32

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

21. Rfc un s`stfgc of sfiunoh hrofn buyc junb`òn of trcnsjfrfnb`c fs5 A ( s ) 

Lp s  s  Lp ;

[fcd`zcr dhs sìu`fntfs bãdbudhs5  Hktfnfr dhs vcdhrfs of L,πn, y ο  fn fn dc fxprfs`òn ifnfrcd of un s`stfgc of sfiunoh hrofn. A ( s ) 

L  n; s  ; n s   n ;

;

 R` sf ofsfc h hktfnfr ktfnfr unc rfspufstc o ofd fd s`stfgc cntf un fsbcdòn bhn un shkrfp`bh of un 3=%. ¸quà vcdhr ofkfr`ã tfnfr Lp Lp8 8  Bhn fd vcdhr of Lp Lp hktfnòh hktfnòh fn fd punth cntfr`hr, ¸buãd sfrçc fd t`fgph of csfntcg`fnth ofd s`stfgc8  R`gudcr fn Gctdck dc rfspufstc scdth of dc p phs`b`òn hs`b`òn cniudcr y (scdòc of dc J_) pcrc vcdhrfs of Lp  =.3,=.;6,;.=,?.=, cofgãs of pcrc fd vcdhr of Lp bcdbudcoh cntfr`hrgfntf.

[fspufstc [f spufstc tfgphr tfgphrcd. cd. R R`stfgcs `stfgcs of hro fn supfr`hr. supfr`h r.

20. Ghthr Rf o`sphnf of dc J_ of un ghthr fdàbtr`bh5 l _

 g ( s ) 

N 3 N ;

F ` ( s )

;

l __ 7=.6, 7 71, Dr 7=.;,E 7=.;,E ffqq7=.=2, j ffqq7=.=;, =.6, l k7=.6,[ r r 71, N35N;7353==

( E s  j fq s )( [r  Dr s )  l t l k s fq

Rf pòf5  [fspufstc cntf unc fntrcoc fn scdth un`tcr`c  [fspufstc cntf unc fntrcoc `gpudsh un`tcr`c  ¸Rf pufof fd`g`ncr cdiõn phdh8  Junb`òn of trcnsjfrfnb`c ofd s`stfgc rfoubòh  [fspufstc `gpudsh un`tcr`c ofd s`stfgc rfoubòh rfoubòh

?=. Ocoh un s`stfgc bhn J_

I ( s) 

3=s  3

s

;

 2s  ;? s  3=

Rf pòf5 3.- Bcdbudcr dhs phdhs y bfrhs ofd s`stfgc. ¸Fs fstckdf fd s`stfgc8 ;.- Bcdbudcr dc rfspufstc fn scdth 2.- ¸Fs phs`kdf rfoub`r fd hrofn ofd s`stfgc8 ?.- @nofpfno`fntfgfntf of dc rfspufstc c dc prfiuntc 2, Bcdbudcr dc rfspufstc c un scdth un`tcr`h ofd s`stfgc of hrofn ; y bhgpcrcr bhn fd hktfnòh fn fd cpcrtcoh ;. 6.- ¸Suà fjfbth t`fnf fd bfrh fn dc rfspufstc ofd s`stfgc8 s`stfgc8

?3. I( s) 

s2

( s  ;)( s ;  2s  3=) 3.- Bcdbudcr dhs phdhs y bfrhs ofd s`stfgc. ¸Fs fstckdf fd s`stfgc8 ;.- Bhgh rfsphnof fstf s`stfgc cntf unc fntrcoc fn scdth 2.- Bhgprufkc tu rfspufstc ofd cpcrtcoh ; bhn Gctdck ?.- ¸Fs phs`kdf rfoub`r fd hrofn ofd s`stfgc8 ¸phr quà8 Ococ un s`stfgc bhn J_

6.- R` rfoubfs fd s`stfgc c unh of hrofn ;, bhgpcrc dc rfspufstc of dcs ohs junb`hnfs of trcnsjfrfnb`c dc hrì`ncd y dc rfoubòc. Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

3?

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[fspufst [f spufst c tfgphrcd. tfgphr cd. R R`st `st fgcs fgcs fn dczh bfrrcoh.

?;. Ofpòs`th bhn rfs`stfnb`c. ]crc fd ofpòs`th of dc jìurc sf ac hktfnòh, trcs d`nfcd`zcr, dcs J_ quf sf gufstrcn _ `

q(t)

qhut

_(t)

_ ( s ) 

 =.2: =.3; S ( s )  Z ( s ) =.3s  3 =.3s  3

Z(t) [

Rf pòf  Bfrrcr fd dczh bhn unc [(s)7Lp, o`kuecr fd o`circgc of kdhqufs fn dczh bfrrcoh, y bcdbudcr dc junb`òn of trcnsjfrfnb`c.  Bcdbudcr fd vcdhr of Lp pcrc quf fd s`stfgc sfc fstckdf  ¸Bògh rfsphnof fd s`stfgc bhn vcdhrfs of Lp7-? y Lp7-3= , cntf unc fntrcoc fn scdth fn dc rfjfrfnb`c8 Bhgprhkcr dc shdub`òn bhn Gctdck.  Bcdbudcr fd frrhr fstcb`hncr`h fstcb`hncr`h cntf un bcgk`h fn dc rfjfrfnb`c of ; unòcof unòcofss  Bcdbudcr fd frrhr fstcb`hncr`h cntf un bcgk`h of 6 unòcofs phr ahrc fn dc pfrturkcb`òn (bcuocd of fntrcoc fn fd tcnquf). ?2. ]crc fd g`sgh ofpòs`th ofd prhkdfgc cntfr`hr ?2.  Bfrrcr cahrc fd dczh bhn unc [(s)7l3/s, o`kuecr fd o`circgc of kdhqufs fn dczh bfrrcoh, y bcdbudcr dc junb`òn of trcnsjfrfnb`c tr cnsjfrfnb`c fn dczh bfrrcoh.  [fshdvfr dc fbucb`òn bbcrcbtfrçst`bc crcbtfrçst`bc ofd s`stfgc fn dcz dczh h bfrrcoh, y bhgprhkcr pcrc o`st`nths vcdhrfs of l3 bhgh rfsphnof fd s`stfgc cntf unc fntrcoc fn scdth.  Bcdbudcr ffdd frrhr fstcb`hncr`h ofd s`stfgc cntf un bcgk`h fn dc rfjfrfnb`c of =.;µB  phr ahrc, y cntf un bcgk`h fn ;µB  fn dc rfjfrfnb`c, bhn un vcdhr of l371 . ??. [fcbthr quçg`bh. Rfc fd rfcbthr quçg`bh of dc jìurc, buyc J_ sf gufstrc _ ( s ) 

6.; s

;

 s  3.=?

V ( s)

 Bfrrcr fd dczh bhn unc [(s)7Lp, o`kuecr fd o`circgc of kdhqufs fn dczh bfrrcoh, y bcdbudcr dc junb`òn of trcnsjfrfnb`c.  [fsufdvf dc fbucb`òn bcrcbtfrçst`bc ofd s`stfgc fn dczh bfrrcoh, y bhgprufkc pcrc o`st`nths vcdhrfs of Lp bhgh rfsphnof fd s`stfgc cntf unc fntrcoc fn scdth.  Bcdbudcr fd frrhr fstcb`hncr`h ofd s`stfg s`stfgc c cntf un bc bcgk`h gk`h fn dc rfjfrfnb`c ofd ;=% phr ahrc bhn unh of dhs L p bcdbudcohs fn fd cpcrtcoh cntfr`hr, y cntf fntrcoc fn fsbcdòn of ; unòcofs. ?6. ]crc fd g`sgh rfcbthr ofd prhkdfgc cntfr`hr ?6.  Bfrrcr fd dczh bhn unc [(s)7=.3/s, o`kuecr fd o`circgc of kdhqufs fn dczh bfrrcoh, y bcdbudcr dc junb`òn of trcnsjfrfnb`c.  [fspufstc ofd s`stfgc fn scdth cntf unc fntrcoc ffnn fsbcdòn of vcdhr unòco.  ¸Rf pufof rfoub`r fd ghofdh fn dczh bfrrcoh8  Bcdbudcr ffdd frrhr fstcb`hncr`h ofd s`stfgc cntf un bcgk`h fn dc rfjfrfnb`c of ;=% phr ahrc bhn unh of dhs Lp bcdbudcohs fn fd cpcrtcoh cntfr`hr, y cntf unc fntrcoc fn fsbcdòn of ; unòcofs. Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

36

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

?:. Fn un prhbfsh of sfbcoh sf `ntrhoubf cd sfbcofrh un b`frth gctfr`cd, eunth bhn unc bhrr`fntf ?:. of c`rf bcd`fntf buyh bcuocd pufof gcn`pudcrsf phr gfo`h of dc sfócd of un s`stfgc vfnt`dcohr. Fstcnoh fn un punth of fqu`d`kr`h, sf rfcd`zc un fxpfr`gfnth bhns`stfntf fn o`sg`nu`r dc sfócd cd vfnt`dcohr un 3%, hksfrvãnohsf un bcgk`h fn dc augfoco ofd gctfr`cd bhgh fd ghstrcoh fn dc jìurc. Rf pòf bcdbudcr dc junb`òn of trcnsjfrfnb`c ofd sfbcofrh. (Pc c v`sth fn s`stfgcs s` stfgcs of sfiunoh hrofn) hr ofn) (P

Vnc vfz bcdbudcoc dc junb`òn of trcnsjfrfnb`c tr cnsjfrfnb`c fn dczh ck`frth I(s).  Bfrrcr fd dczh bhn un rfiudcohr [(s)7Lp. O`kuecr fd o`circgc of kdhqufs ofd s`stfgc fn dczh bfrrcoh, y bcdbudcr dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh.  Bcdbudcr fd vcdhr of dc icncnb`c ofd rfiudcohr pcrc hktfnfr un frrhr fstcb`hncr`h `njfr`hr cd =.3 % fn dc rfspufstc fn dczh bfrrcoh c un scdth ofd ;% fn dc rfjfrfnb`c  Bcdbudcr fd vvcdhr cdhr of dc icncnb`c ofd rfiudcohr pcrc hktfnfr un shkrfp`bh shkrfp`bh ofd ;=% fn dc rfspufstc fn dczh bfrrcoh c un scdth of ohs unòcofs fn dc rfjfrfnb`c. ?9. Rf vc c o`sfócr un s`stfgc of dczh bfrrcoh pcrc quf prhouzbc, cntf unc fntrcoc fsbcdòn, unc ?9. rfspufstc sukcghrtìucoc. Dcs fspfb`j`bcb`hnfs shn5 • Vn shkrf`gpudsh (fn %) bhgprfnoòh fntrf fntrf un 3=% y u un n ;=%. • Vn t`fgph of fstckdfb`g`fnth fstckdfb`g`fnth gfnhr of =.: s, bhn fd br`tfr`h ofd ;%. Rf pòf5 3. @ofnt`j`bcr fd ãrfc ofsfcoc pcrc dcs rcçbfs ohg`ncntfs ofd s`stfgc. ;. Oftfrg`ncr fd vc vcdhr dhr gãs pfqufóh pfqufóh of unc tfrbfrc rcçz rcçz r 2 s` dcs rcçbfs bhgpdfecs bhneuicocs rfprfsfntcn dhs phdhs ohg`ncntfs. Rf sckf quf dc junb`òn of trcnsjfrfnb`c fs of 2fr hrofn y dc icncnb`c of rfcd`gfntcb`òn fs 3. Oftfrg`nf I(s) pcrc tfnfr un t`fgph of fstckdfb`g`fnth of =.:s (;%) y un shkrfpcsh ofd ;=%. ?1.   Ofghstrcr quf fd frrhr fstcb`hncr`h cntf fntrcocs rcgpc pufof acbfrsf ìucd c bfrh, s` dc ?1. c n 3 s  c n junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh fs5 B ( s )  n n 3 [ ( s ) s  c3 s      c n 3 s  c n ?0.  ]crc fd s`stfgc of dc jìurc ?0.

Y(s) +

-

L

P(s) I(s)

I( s) 

; 3  ;s

A ( s ) 

2.6 s  2.6

A(s)

c) Hktfnic fd vcdhr gçn`gh of dc bhnstcntf L pcrc quf fn rài`gfn pfrgcnfntf fd frrhr fstcb`hncr`h sfc gfnhr quf fd 3=% cntf unc fntrcoc fsbcdòn. k) ]crc fsf vcdhr of L, oftfrg`nf fd bhfj`b`fntf of cghrtìucg`f cghrtìucg`fnth nth y dc jrfbufnb`c ncturcd nh cghrtìucoc. b) ¸Fx`stf cdiõn vcdhr of L pcrc fd qu quf f sf bugpdc dc bhno`b`òn ofd 3=% 3=% y fd s`stfgc nh sfc hsb`dcthr`h8 Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

3:

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

6=. Vn s`stfgc fn dczh bfrrcoh bhn rfcd`gfntcb`òn un`tcr`c t`fnf unc junb`òn of trcnsjfrfnb`c o`rfbtc5

s ;  2s  ;

Bcdbudcr fd vcdhr ofd frrhr fstcb`hncr`h cntf unc fntrcoc fsbcdòn s ?  ;s 2  s ;  2s  3 un`tcr`h, cncd`zcr dc fstck`dòco y bhgfntcr dhs rfsudtcohs.

I(s) 

63. (Bufst`òn 3. Fxcgfn fxtrchro`ncr`h 33-3;). Dcs sìu`fntfs irãj`bcs gufstrcn dc rfspufstc fn dczh bfrrcoh of buctrh s`stfgcs bhn rfcd`gfntcb`òn un`tcr`c nfict`vc. Fn bcoc irãj`bc sf `no`bc fd t`ph of fntrcoc cpd`bcoc. Rf pòf5  C pcrt`r of dc rfspufstc ghs ghstrcoc, trcoc, ofoub`r f fdd t`ph ofd s`stfgc y s` acy f frrhr rrhr fstcb`hncr`h, h nh.  Fn bcsh of quf acyc frrhr fstcb`hncr`h, bcdbudcrdh.

36

=.3

=.=0 =.=1 =.=9

3=

=.=:

Cgpd`tuo

Cgpd`tuo

=.=6 =.=?

6

=.=2 =.=;

=.=3

=

=

=

=.3

=.;

=.2

_`fgph (sfiunohs)

=.?

=.6

=.:

3=

=.0 =.1 =.9 =.: Cgpd`tuo =.6 =.? =.2 =.; =.3

36

Jìurc 25 [fspufstc ofd R`stfgc 2 cntf 2 cntf fntrcoc rcgpc un`tcr`c

3



6

_`fgph (sfiunohs)

3 cntf cntf fntrcoc scdth un`tcr`h Jìurc 35 [fspufstc ofd R`stfgc 3

==

=

:

6

? Cgpd`tuo 2

;

3

3

;

2

6 : _`fgph 9 (sfiunohs)

?

1

0

3=

Jìurc ;5 [fspufstc ofd R`stfgc ; cntf ; cntf fntrcoc scdth un`tcr`h

==

=.6



3 3.6 _`fgph (sfiunohs)

;

;.6

Jìurc ?5 [fspufstc ofd R`stfgc ? ? cntf cntf fntrcoc scdth un`tcr`h

6;. Fd o`circgc of kdhqufs of un ghthr bhntrhdcoh phr crgcourc fs fd of dc jìurc. j ìurc. Rf pòf c) Oftfrg`ncr fd frrhr fn fstcoh fstcb`hncr`h cntf unc fntrcoc fsbcdòn y cntf unc fntrcoc rcgpc un`tcr`c fn tàrg`nhs of L , L k, y L g. k) Rfc L g73=   y y L k7=.=6 , sfdfbb`hncr L  pcrc pcrc quf fd frrhr fstcb`hncr`h vcdic 3. b)]crc dhs vcdhrfs cntfr`hrfs o`kuecr dc rfspufstc cntf unc fntrcoc fsbcdòn y unc rrcgpc cgpc un`tcr`c. [(s) +

L

N(s) +

-

-

L g (s+=.==3)

B(s )

3 s

P(s )

Lk

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

39

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

62. (Bufst`òn ;. Fxcgfn hro`ncr`h 33-3;). Cncd`zcr fd fjfbth quf dc vcr`cb`òn ofd pcrãgftrh _` (_`>=) (_`>=) prhoubf fn fd frrhr fstcb`hncr`h ofd s`stfgc of dc jìurc fn fd bcsh of fntrcocs t`ph5 (3)fsbcdòn (Y(s)73/s) (Y(s)73/s) y y (;)rcgpc (Y(s)73/s;  ) ).. Rupònicsf quf fd s`stfgc I(s) pufof tfnfr5 (C) bfrh, (K) unh h (B) ohs phdhs fn fd hrìfn.   3 ]@O ( s )  L  p 3   _ o s  Y(s)

F(s) + -

V(s) ]@O(s)



P(s) I(s)

g

 I( s) 

k` s

s

c s



g

 s  z 

`

= n  N N

_ ` s

`

e

 L

e

=

= n  N

N

s

 s  p 

e

=

6?. (]rhkdfgc 3. Fxcgfn fxtrchro`ncr`h 33-3;). Vn surtòhr of icshd`nc pufof ghofdcrsf gfo`cntf dc fbucb`òn5 ;

oS(t )

 u (t )  ?¹S ; (t )  S(t ) .

ot Ohnof S(t) fs fd bcuocd of icshd`nc quf oc fd surtòhr (d`trhs/sfiunoh) y u(t) fs dc tfns`òn of fntrcoc cd ghthr of dc khgkc ofd surtòhr (vhdt`hs), quf sf pufof gcn`pudcr c vhduntco. Rf bhnstruyf un s`stfgc of bhntrhd pcrc rfiudcr fd vhdugfn of icshd`nc sug`n`strcoc, Z(t). ]crc fddh sf pdcntfc fd s`stfgc of bhntrhd of dc jìurc.

rfj . Fn o`bah fsqufgc fd vhdugfn of d`trhs d` trhs ofsfcohs fs RfZsckf quf dc rfdcb`òn fntrf fd vhdugfn y fd bcuocd of icshd`nc sug`n`strcoh phr fd surtòhr v`fnf ocoh phr dc sìu`fntf fbucb`òn o`jfrfnb`cd

oZ (t ) ot

 S (t ) .

c) Fdfiòh fd punth of trckceh S7=. d`trhs/sfiunoh, bcdbudf dc junb`òn of trcnsjfrfnb`c quf rfdcb`hnc fd vhdugfn of icshd`nc sug`n`strcoh phr fd surtòhr bhn dc tfns`òn of cd`gfntcb`òn of dc khgkc ofd surtòhr (I(s) fn dc jìurc. k) ]crc [(s)7L, fnbufntrf dhs vcdhrfs of L quf icrcnt`zcn dc fstck`dòco ofd s`s s`stfgc tfgc of bhntrhd. b) ]crc fd rcnih of vcdhrfs o of f L fn dhs quf fd s`stfgc of bhntrhd bhntrhd fs fstckdf, rczhnf fd t`ph of rfspufstc ofd s`stfgc fn dczh bfrrcoh fn junb`òn of dhs vcdhrfs of L. o) ]crc L7=.=?6, rczhnf s` pufof rfoub rfoub`r `r fd hrofn of dc junb`òn of trcnsjfrfnb`c ofd s`stfgc fn dczh bfrrcoh. R` jufsf csç, rfouzbc o`bac junb`òn of trcnsjfrfnb`c f `no`quf dhs pcrãgftrhs bcrcbtfrçst`bhs of dc junb`òn of trcnsjfrfnb`c rfoubòc y o`kuef dc rfspufstc ofd s`stfgc cntf un fsbcdòn un`tcr`h.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

31

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[fspufst [f spufst c fn j rfbufnb`c.

66. Ofpòs`th bhn rfs`stfnb`c. ]crc fd ofpòs`th of dc jìurc sf ac hktfnòh, trcs d`nfcd`zcr, dcs J_ 66. quf sf gufstrcn _ `

q(t)

qhut

_ ( s ) 

_(t)

=.3;  =.2: S ( s )  Z ( s ) =.3s  3 =.3s  3

Z(t) [

Rf pòf  ¸Bògh fs dc rfspufstc tfgphrcd fstcb`hncr`c bucnoh sf cp cpd`bc d`bc unc tfns`òn Z(t)7;sfn(2t)8  Bhgprhkcr fd rfsudtcoh bhn R`gud`nl y Gctdck.  O`kuecr fd O O`circgc `circgc of Khof cs`ntòt`bh. Bhgpcrcrdh bhn fd quf prhphrb`hnc Gctdck. Gctdck. Acddcr fd cnbah of kcnoc ofd s`stfgc. 6:.  B`rbu`th [DB. 6:. Z(s)

ZB(s)

3 DBs  [Bs  3 ;

 Bhgh ffss dc rfspufstc oofd fd b`rbu`th c unc fntrcoc fn s`nushòcd Z(s)7: s`n(t) bhn [7; , D73 y B7=.=?. Bhgprufkc fd rfsudtcoh fn Gctdck.  O`kuecr fd O`circgc of Khof cs`ntòt`bh. cs`ntòt`bh. ¸Acy rfshncnb`c8 Fn fsf bcsh bcdb bcdbudcr udcr dc jrfbufnb`c y fd p`bh of rfshncnb`c.  Bhgprhkcr dhs rfsudtcohs bhn Gctdck. 69. B 69. hnhbòc dc junb`òn of trcnsjfrfnb`c5 I ( s)  3=

   

s

;

s  3  9 s  3=

O`kuecr fd O`circgc of Khof (cs`ntòt`bh). Bcdbudcr cnbah of kcnoc. ¸Acy rfs rfshncnb`c8 hncnb`c8 R R`` fs b`frth bcdbudcr dc jrfbufn jrfbufnb`c b`c of rfshncnb`c y fd p p`bh `bh of rfshncnb`c. Bhgprhkcr dhs rfs rfsudtcohs udtcohs bbhn hn Gctdck (o`kuecr O`c O`circgc ircgc of Khof y of Nyqu`st).

61. O 61. coh fd o`circgc of Khof of dc jìurc, c quà junb`òn of trcnsjfrfnb`c bhrrfsphnof. ( s  6) I( s )  ; s ( s  3) ; KhofO`circg

36=

3==

6=    )    K    o    (   f    o   u    t    `   n   i   c    G

=

I ( s) 

-6=

-3==

( s  6) s( s  =.=3)(s  2=)

-36= -0=

I( s)     )   i   f    o    (   f   s   c    a    ]

-326

-31= -?

3=

-2

3=

-;

3=

-3

=

3=

3=

3

3=

;

3=

Jrfqufnby (rco/s)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

2

3=

I(s) 

( s  6) s ; ( s  =.=3)( s  2=)

( s 6) s ; ( s  =.=3)( s  3)

30

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

60. (Bufst`òn 2. Fxcgfn fxtrchro`ncr`h bursh 33/3;). Bhnsòfrf un s`stfgc buyc rfspufstc fn jrfbufnb`c fs dc bhrrfsphno`fntf cd o`circgc of khof coeunth. c) Oftfrg`nf of jhrgc c cprhx`gcoc prhx`gcoc fd cnba cnbah h of kcnoc o ofd fd s`stfgc. k) Oftfrg`nf of jhrgc c cprhx`gcoc prhx`gcoc dc icnc icncnb`c nb`c fstãt`bc, fn dcs unòcofs of dc junb`òn of trcnsjfrfnb`c ofd s`stfgc. b) R` o`bah s`stfgc f fs s fxb`tcoh bh bhn n unc sfócd s`nushòcd of cgpd`tuo ;.6 y jrfbufnb`c =.2312 afrb`hs. ¸Buãd fs dc fxprfs`òn of dc scdòc ofd s`stfgc, fn rài`gfn fstcb`hncr`h8

:=. (Bufst`òn ;. Fxcgfn hro`ncr`h 3;-32). Oftfrg`ncr buãd of dcs sìu`fntfs junb`hnfs of trcnsjfrfnb`c fs dc quf bhrrfsphnof bhn fd o`circgc of Khof. Eust`j`bcr dc rfspufstc.

I ( s) 

6=s  3= 

s  6=s  3

I( s ) 

(c)

6=s  3= ss  6=s  3

I( s ) 

s  3= ss  6=s  3

(k)

I ( s) 

(b)

6=3=s  3 ss  6= s  3

(o)

O`circgc of Khof

3==

6=    )    K    o    (    o   u    t    `   n   i   c    G

=

-6=

-3== -0=

   )   i   f    o    (   f   s   c    J

-326

-31= -; 3=

-3

3=

=

3

3=

3=

;

3=

2

3=

Jrfbufnb`c (rco/s)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;=

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

:3. (Bufst`òn 3. Fxcgfn hro`ncr`h 33-3;). ;s  2

Ocoh fd s`stfgc buyc junb`òn of trcnsjfrfnb`c tr cnsjfrfnb`c fs I ( s ) 

s  2s ;  s  2

3.- ¸Fs phs`kdf rfoub`r su hrofn8 ¸]hr quà8 Fn bcsh of quf pufoc acbfrsf hktfnic dc junb`òn of trcnsjfrfnb`c ofd s`stfgc rfoubòh. ;.- @no`quf buãd of dhs sìu`fntfs o`circgcs of Khof bhrrfsphnof bhn àd y eust`jçqufdh. O`circgc of Khof

O`circgc of Khof

=    )    K    o    (   f    o   u    t    `   n   i   c    G

6=    )    K    o    (   f    o   u    t    `   n   i   c    G

-6=

-3== -326    )   i   f    o    (   f   s   c    a    ]

= -6= -3== -?6

   )   i   f    o    (   f   s   c    a    ]

-31= -;;6 -;9=

-0= -326 -31= -;;6

-;

3=

-3

=

3=

3

3=

3=

;

(c)

-3

3=

3=

O`circgc of Khof    )    K -;=    o    (   f    o -?=   u    t    `   n   i   c -:=    G

   )    K    o    ( =   f    o   u    t    `   n -;=   i   c    G

-1= =

-?= ?6    )   i   f    o    (   f   s   c    a    ]

-?6 -0= -326 -3

3=

=

3

3=

;

3=

O`circgc O`circgc of Khof ;=

-31=

3

3=

(k)

=

   )   i   f    o    (   f   s   c    a    ]

=

3=

3=

(b)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;

3=

= -?6 -0= -326 -3

3=

=

3

3=

3=

;

3=

(o)

;3

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[fspufstc fn jrfbufnb`c fn Dczh Bfrrcoh. Fstck`dòco rfdct`vc.

:;. Ofpòs`th bhn rfs`stfnb`c. ]crc fd ofpòs`th of dc jìurc sf ac hktfnòh, trcs d`nfcd`zcr, dcs J_ quf sf gufstrcn

_ `

q(t)

qhut _ ( s ) 

Z(t) [

 =.2:

S ( s ) 

=.3s  3

_(t)

=.3;

Z ( s )

=.3s  3

;3

;=.1

;=.:

;=.?

;=.;

;=

30.1 30.:

30.?

30.;

30 =

3

;

2

?

6

:

9

1

0

3=

c) Bhnsòfrcnoh quf bfrrcghs fd dczh bhn un rfiudcohr [(s)7L73=. R`, trckcecnoh fn dczh bfrrcoh, dc rfjfrfnb`c fxpfr`gfntc bcgk`hs s`nushòcdfs bhgh fn dc Jìurc , ¸Bògh sfrã dc scdòc cd bckh of un t`fgph8. k) Bhgpcrc dhs rfsudtcohs s` dh acbfghs fn Gctdck b) O`kuec fd o`circgc of Nyqu`st ofd s`stfgc fn dczh ck`frth fn Gctdck, y bcdbudc fd gcrifn of icncnb`c y fd gcrifn of jcsf c gcnh. Bhgpcrc fd rfsudtcoh s` dh acbfs cuthgãt`bcgfntf bhn GC_DCK. o) O`kuec fd o`circgc of Khof of ofdd s`stfgc fn dczh ck`frth, y bcdbudc dhs gãrifnfs gãrifnfs of jcsf y icncnb`c of fstf s`stfgc. Bhgpãrcdhs bhn dhs rfsudtcohs ofd cpcrtcoh b).

:2. ]crc fd ghofdh ofd prhkdfgc cntfr`hr. 3. Bhnsòfrcnoh quf bfrrcghs fd dczh bhn u un n rfiudcohr [(s)7L/s71/s [(s)7L/s71/s.. R`, trckcecnoh fn dczh bfrrcoh, dc rfjfrfnb`c fxpfr`gfntc bcgk`hs s`nushòcdfs bhgh fn dc Jìurc , ¸Bògh sfrã dc scdòc cd bckh of un t`fgph8. ;. Bhgpcrc dhs rfsudtcohs s s`` dh ac acbfghs bfghs fn Gctdck 2. O`kuec fd o`circgc of Nyqu`st ofd s`stfgc fn dczh ck`frth fn Gctdck, y bcdbudc fd gcrifn of icncnb`c y fd gcrifn of jcsf c gcnh. Bhgpcrc fd rfsudtcoh s` dh acbfs cuthgãt`bcgfntf bhn GC_DCK. ?. O`kuec fd o`circgc of Khof of ofdd s`stfgc fn dczh ck`frth, y bcdbudc dhs gãrifnfs gãrifnfs of jcsf y icncnb`c of fstf s`stfgc. Bhgpãrcdhs bhn dhs rfsudtcohs ofd cpcrtcoh b).

:?. Vt`d`zcr dcs trczcs of Khof y/h o`circgc of Nyqu`st pcrc oftfrg`ncr fd gcrifn of L ofntrh ofd bucd fs fstckdf fd s`stfgc fn dczh bfrrcoh.

[(s) +

  -

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

L

3

P(s)

( s  ;)( s  ?)( s  6)

;;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

:6.O :6. `kuecr unc cprhx`gcb`òn of dhs d hs o`circgcs of Khof y Nyqu`st of dcs ohs junb`hnfs fn dczh of ck`frth quf sf `no`bcn. Fstuo`cr dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh

I3 ( s ) 

;=s  6

s  3 s  3= 

I; ( s ) 

;= s  6 

[(s) +

-

s  3 s  3= 

I(s)

B(s)

::.( ]rhkdfgc ;. Fxcgfn hro`ncr`h 33-3;). ::. Bhnsòfrf fd s`stfgc of bhntrhd of dc Jìurc 3, ohnof [( s ) 

Lb

(3  3==s )

, y I(s) fs dc junb`òn of

trcnsjfrfnb`c ofd s`stfgc buyc rfspufstc fsbcdòn fs dc of dc Jìurc ;.

Jìurc 3 Jìurc ; c) Acddcr I(s). k) ]crc Lb73= , o`kuecr fd o`circgc of Khof cs`ntòt`bh quf df pfrg`tc fstuo`cr dc fstck`dòco fd s`stfgc of bhntrhd of dc Jìurc 3. C pcrt`r of fsf o`circgc, oftfrg`nf of jhrgc cprhx`gcoc dhs vcdhrfs of dhs gãrifnfs of jcsf y icncnb`c ofd s`stfgc of bhntrhd. Fn kcsf c dhs g`sghs, rczhnf dc fstck`dòco ofd s`stfgc of bhntrhd. b) Fn fd bcsh of quf pcrc Lb73=   fd s`stfgc fn dczh bfrrcoh rfsudtf fstckdf, bcdbudf fd frrhr fstcb`hncr`h cntf unc fntrcoc fsbcdòn of vcdhr 6 . Fn fd bcsh of quf pcrc Lb73=  fd fd s`stfgc fn dczh bfrrcoh sfc `nfstckdf, oftfrg`nf dhs vcdhrfs of Lb quf icrcnt`zcn dc fstck`dòco ofd g`sgh.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

;2

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

:9. (Bufst`òn 2. Fxcgfn hro`ncr`h 33-3;). c) Ocoh fd s`stfgc bhn rfcd`gfntcb`òn un`tcr`c of dc jìurc, su o`circgc of Khof (J_ fn dczh ck`frth) fs fd quf sf gufstrc. Hktfnic dhs gãrifnfs of jcsf y of icncnb`c. I s  

;===( s  =.3)

s  :s  ;s  3=

Y(s) +

I

Y(s) +

3 Ibs   3  3=s

k). Rf df cpd`bc un bhntrhdcohr ]@

B(s)

B(s )

I

Ib

-

Hktfnic fd nufvh o`circgc of Khof y dhs nufvhs gãrifnfs of jcsf y icncnb`c. ¸Buãd fs dc pr`nb`pcd vfntcec ofd s`stfgc bhgpfnscoh8 ?= 2=

;=

?.? = 3=

-3=

-;=

-2= -?=

-6=

-2

-:= 3=

-3

-;

3=

3=

3=

=

3=

;

3

3=

3=

2

3== 6= = -6= -3== -36= -;== -2 3=

-;

3=

-3

=

3=

3

3=

;

3=

3=

2

3=

:1. (]rhkdfgc ;. Fxcgfn fxtrchro`ncr`h 33-3;). Ocoh fd s`stfgc rfcd`gfntcoh of dc jìurc

](s) [(s) +

-

L s

V(s)

I7

(s+;) (s+3)

+ +

P(s)

c) Bcdbudf dcs junb`hnfs o of f trcnsjfrfnb trcnsjfrfnb`c5 `c5 P( P(s s)/[( )/[(s s), P(s P(s)/]( )/](s s) y V(s V(s)/[( )/[(s s). k) Oftfrg`nf cprhx`gcocgf cprhx`gcocgfntf, ntf, pcrc L73, dhs gãri gãrifnfs fnfs of jcsf y of icncnb`c ofd s`stfgc. b) Bcdbudf fd rcnih of vcdhrfs of L quf acbfn qu quf f s`gudtãnfcgfntf5 Fd frrhr fstcb`hncr`h cntf u unc nc fntrcoc rcgpc un`tcr`c fn [ sfc gfnhr qu quf f =.3< Cntf u unc nc fntrco fntrcoc c scdth tfnic un t`fgph o of f fstckdf fstckdfb`g`fnth b`g`fnth gf gfnhr nhr quf ; sfiu sfiunohs. nohs.   



Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;?

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

:0. (]rhkdfgc. Fxcgfn hro`ncr`h 3;-32). Vn prhbfsh of sfbcoh (fd`g`ncb`òn of augfoco) cpd`bc un jdueh of c`rf bcd`fntf (gfo`cntf unc sfócd =…..3==% c un s`stfgc vfnt`dcohr), c dc bãgcrc of sfbcoh fn ohnof sf fnbufntrc fd gctfr`cd c sfbcr. Fstcnoh fn un punth of fq fqu`d`kr`h, u`d`kr`h, sf rfcd`zc un fxpfr`gfnth bhns`stfntf bhns`stfntf fn o`sg`nu`r dc sfócd cd vfnt`dcohr un 3%, hksfrvãnohsf un bcgk`h fn dc augfoco ofd gctfr`cd bhgh fd ghstrcoh fn dc jìurc.

Rf pòf5 c) ]crc bhntrhdcr dc augfoco sf usc un bhntrhdcohr t`ph ]. O`kuecr un un o`circgc of kdhqufs ofd s`stfgc of bhntrhd rfsudtcntf fn dczh bfrrcoh, fspfb`j`bcnoh dcs junb`hnfs of trcnsjfrfnb`c. k) Bcdbudcr fd vcdhr of dc icncnb`c ofd rfiudcohr pcrc hktfnfr un shkrfp`bh ofd ;=% fn dc rfspufstc fn dczh bfrrcoh c un scdth of ohs unòcofs fn dc rfjfrfnb`c. b) Bcdbudcr fd vcdhr of dc icncnb`c ofd rfiudcohr pcrc h hktfnfr ktfnfr un frrhr fs fstcb`hncr`h tcb`hncr`h `njfr`hr cd =.3 % fn dc rfspufstc fn dczh bfrrcoh c un scdth ofd ;% fn dc rfjfrfnb`c . ¸Buãd sfrã fd vcdhr fstcb`hncr`h of dc vcr`ckdf of scdòc y of dc vcr`ckdf gcn`pudcoc fn fstf bcsh8. ]crc fstc pcrtf rfbufroc bcdbudcr dcs o`st`ntcs junb`hnfs of trcnsjfrfnb`c ofd s`stfgc. P(s)/[(s) y V(s)/[(R). o) Bcdbudc fd gcrifn of jcsf y fd gcrifn of icncnb`c pcrc fd s`stfgc uscnoh fd rfiudcohr bcdbudcoh fn fd cpcrtcoh 2, rczhnc r czhnc shkrf dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;6

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Duicr of dcs rcçbfs.

9=. Ofpòs`th bhn rfs`stfnb`c. ]crc fd ofpòs`th of dc jìurc sf ac hktfnòh, trcs d`nfcd`zcr, dcs J_ quf sf gufstrcn _ `

q(t)

qhut

_(t) Z(t) [

f) Fstuo`cr dc fstck`dòco y dcs bcrcbtfrçst`bcs of dc rfspufstc ofd s`stfgc fn dczh ck ck`frth `frth y fn dczh bfrrcoh cntf unc fntrcoc fsbcdòn un`tcr`h fn Y(s), bucnoh sf b`frrc fd dczh bhn un rfiudcohr Lp. Bcdbudcr un Lpc ofbucoh. j) O`kuecr fd duicr of dcs rcçbfs. i) Fstuo`cr fd g`sgh bbcsh csh s` fd dczh sf b`frrc bhn un rfiudcohr ]@, ¸Buãn ¸Buãnth th vcdf Lp y _` 8 ¸Bògh fs dc rfspufstc ofd s`stfgc fn dczh bfrrcoh cntf unc fntrcoc fsbcdòn fn Y(s) bhn fsf Lp y _` bcdbudcoh bhn fd duicr of dcs rcçbfs8 Bhgprhkcrdh fn Gctdck. 93.   Ocoh 93. I ( s) 

fd L

s`stfgc

of

dc

jìurc,

ohnof

[(s)

F(s)

-

I(s)

B(s)

, L73, A(s)73.

A(s) s  6s  ? Fstuo`cr dc fstck`dòco y dcs bcrcbtfrçst`bcs of dc rfspufstc ofd s`stfgc fn dczh ck`frth y fn dczh bfrrcoh cntf unc fntrcoc fsbcdòn un`tcr`h fn [(s). ¸Suà subfof subfof s` L thgc htrhs vcdhrf vcdhrfs8 s8 ;

9;.   Ocoh 9;. I( s) 

fd s`stfgc of dc L ( s  6) s ;  2s  ;? , A(s)73.

jìurc,

ohnof

[(s)

F(s)

-

I(s)

B(s)

A(s)

Fstuo`cr dc fstck`dòco y dcs bcrcbtfrçst`bcs of dc rfspufstc ofd s`stfgc fn dczh bfrrcoh cntf unc fntrcoc fsbcdòn un`tcr`h fn [(s). 92.  ]crc fd s`stfgc of dc jìurc 92.

Y(s) +

  -

L  p

(s  :)  (s 2)(s  =.6)(s  ;)

P(s)

3.- Bcdbudcr fd duicr of dcs rcçbfs ;.- Acddcr dhs punths of rupturc y dcs csçnthtcs. 2.- Acddcr dhs phdhs ohg`ncntfs ofd s`stfgc quf acbfn quf fd s`stfgc junb`hnf bhn un shkrfpcsh ofd 36%, fd vcdhr of Lp pcrc hktfnfr fshs phdhs y dc phs`b`òn ofd 2fr phdh. ?.-Oftfrg`ncr fd vcdhr of Lp quf acbf quf fd s`stfgc sfc brçt`bcgfntf cghrtìucoh y fd vcdhr of Lp quf acbf quf sfc brçt`bcgfntf fstckdf 6.-Hktfnfr dc rfspufstc fsbcdòn ofd s`stfgc fn dczh bfrrcoh pcrc fd vcdhr of Lp hktfnòh fn fd cpcrtcoh 2 y bhgprufkf bucd fs rfcdgfntf r fcdgfntf fd vcdhr ofd shkrfpcsh. :.-Rf ofsfc quf fd s`stfgc prfsfntf un frrhr fstcb`hncr`h gfnhr quf =.=3 cntf unc fntrcoc fsbcdòn. Oftfrg`ncr fd vcdhr ofd shkrfpcsh g gãx`gh ãx`gh quf sf hkt`fnf gcntfn`fnoh gcntfn`fnoh fstf frrhr.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

;:

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

9?. ]crc fd s`stfgc of dc jìurc

Y(s) +

L  p

  -

P(s)

3 (s ;  6s  ?)(s  2)

3.- Bcdbudcr fd duicr of dcs rcçbfs ;.- Fstuo`cr dc fstck`dòco y dc rfspufstc fn dczh ck`frth y dczh bfrrcoh of fstf s`stfgc.

96. (Bufst`òn ?. Fxcgfn hro`ncr`h 3;-32). Rfc un s`stfgc of dc jhrgc5

[(s) +

L

-

P(s)

I(s)

A(s)

c) C pcrt`r of dhs duicrfs of dcs rcçbfs of dcs jìurcs rczhncr buãdfs t`fnfn junb`hnfs of trcnsjfrfnb`c fn dczh bfrrcoh quf shn s`fgprf fstckdfs y buãdfs nh. Cofgãs `no`bcr s` dc fstck`dòco sf prhoubf pcrc vcdhrfs of dc icncnb`c L pfqufóhs h ircnofs. Eust`j`bcr dc rfspufstc. k) Fdfi`r unh of dhs duicrfs o of f dcs rcçbfs ghstrcohs fn dcs dcs jìurcs y, suphn`fnoh A(s)73, ofoub`r dc junb`òn of trcnsjfrfnb`c fn dczh d czh bfrrcoh. [hht Dhbus

: H

?

   )

   3     s

   o   n   h   b   f   s    (

  s    `   x    C

  y   r   c   n    `   i   c   g    @

;

=

H

Q

Q

Q

-;

-? H

-: - 3;

- 3=

-1

-:

-? [fcd Cx`s (sfbhnos

-3

-;

=

;

)

R`stfgc (3)

[hht Dhbus

36

3=

H Q

   )

6

   3     s

   o   n   h   b   f    (   s   s    `   x    C   y   r   c   n    `   i   c   g    @

=

H

Q

H

Q

-6 Q

-3=

-36 -3;

H

-3=

-1

-:

-?

-;

=

;

[fcd Cx`s (sfbhnos -3)

R`stfgc (;)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;9

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[hht Dhbus

;= 36 3=    )

   3     s

6

   o   n   h   b   f   s    (

  s    `   x    C

  y   r   c   n    `   i   c   g    @

=

Q

Q

Q Q

H

-6 -3= -36 -;= -2=

-;6

-;=

-36

-3=

-6

=

6

3=

-3

[fcd Cx`s (sfbhnos )

R`stfgc (2)

[hht Dhbus

2=

;=

   )

3=

Q

   3     s

   o   n   h   b   f   s    (

  s    `   x    C   y   r   c   n    `   i   c   g    @

H

=

Q

Q H

-3=

Q

-;=

-2= - 3;

-3=

-1

-:

-?

-;

=

;

?

:

1

[fcd Cx`s (sfbhnos -3)

R`stfgc (?)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;1

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

O`sfóh O`sfó ho of f ]@ ]@O. O.

9:. Bucnoh c un s`stfgc sf df cpd`bc unc fntrcoc fsbcdòn of cgpd`tuo unh (rfspfbth of su fstcb`hncr`h 3.6), su rfspufstc qufoc bhgh dc ghstrcoc fn dc jìurc. 3.:6 3.:?

3.:;

3.:

3.61   f    o   u    t    `    d   p   g    C

3.6:

3.6?

3.6;

3.6

3.?1 -3

-=.6

=

=.6

3

3.6

;

;.6

2

2.6

?

?.6

6

6.6

:

:.6

9

_`gf (sfb hnos)

Rf pòf5 Fst`gcr dc icncnb`c L , fd rftcroh o  y y dc bhnstcntf of t`fgph  of su cprhx`gcb`òn phr un s`stfgc of pr`gfr hrofn bhn rftcroh. r ftcroh. C pcrt`r of o`bah ghofdh o`sf o`sfócr ócr un bhntrhdcohr ], un ]@ y un ]@O sìu`fn sìu`fnoh oh dcs tckdcs v`stc v`stcs s fn bdcsf of _fhrçc, of U`fidfr-N`bahds fn dczh ck`frth. R` sf sckf quf fsc rfspufstc sf bhrrfsphnof bhn dc J J_ _ fn dczh ck`frth 





I( s) 

3 s  :s  3; s  1 2

;

, cncd`zcr fd bhgphrtcg`fnth ofd s`stfgc fn dczh bfrrcoh (fstcb`hncr`h

ofd s`stfgc bhn dhs o`st`nths bhntrhdcohrfs acddcohs) —fn bcoc bcsh‗ (fvhdub`òn of scdòc y sfócd of bhntrhd cntf bcgk`hs t`ph scdth fn dc rfjfrfnb`c y pfrturkcb`hnfs fn dc scdòc t`ph scdth), y bhgprhkcr dhs rfsudtcohs fn Gctdck/R`gud`nl.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

;0

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

FNVNB@COHR OF FQCGFN. Fxcgfn Fxcgf n hro` hr o`ncr`h ncr`h (eun`h). (eun `h). Bur Bursh sh 33-3; 33-3; ][HKDFGC 3 (; ]VN_HR)

Dc jìurc rfjdfec un prhbfsh of bcdfntcg`fnth of un jduòh. Fd jduòh ddfic cd o`sphs`t`vh `ntfrbcgk`co `ntfrbcgk`cohr hr of bcdhr c unc tfgpfrcturc _` (µB) (quf pufof vcr`cr bhn fd t`fgph), y ofspuàs ofd prhbfsh of bcdfntcg`fnth bcdfntcg`fnth scdf bhn unc tfgpfrcturc _ (µB). Rf o`sphnf of unc vãdvudc of rfiudcb`òn quf pufof gho`j`bcr fd bcuocd ofd jduòh (q) quf b`rbudc phr fd o`sphs`t`vh `ntfrbcgk`cohr. Rf ofnhg`nc u (%) c dc cpfrturc of o`bac vãdvudc. Fd ghofdh gctfgãt`bh quf pfrg`tf bcdbudcr dc fvhdub`òn of dc tfgpfrcturc of scdòc ofd jduòh fn junb`òn of dc tfgpfrcturc of fntrcoc y of dc cpfrturc of dc vãdvudc of rfiudcb`òn fs5   2   : :  1.1 1.1  ; 

Bucnoh fd s`stfgc fstã fn fstcoh fstcb`hncr`h y dc tfgpfrcturc of fntrcoc fs of 3= µB, dc of scdòc fs of ?=µB. Rf pòf5 3) @ofnt`j`bcr dcs vcr`ckdfs ofd prhkdfgc5 ¸Buãd fs dc fntrcoc8, ¸buãd fs dc scdòc8 y ¸buãd fs dc pfrturkcb`òn8 (=.;) ;) Bhn dc fbucb`òn o`jfrfnb`cd ococ cntfr`hrgfntf bcdbudcr dc junb`òn of trcnsjfrfnb`c of dc scdòc rfspfbth of dc fntrcoc, y dc junb`òn of trcnsjfrfnb`c of dc scdòc rfspfbth of dc pfrturkcb`òn. O`kuecr fd o`circgc of kdhqufs ofd s`stfgc bhnsòfrcoh, bhn sus junb`hnfs of trcnsjfrfnb`c. (=.:) 2) Rf prftfnof bhntrhdcr dc tfgpfrcturc of scdòc ofd jduòh uscnoh un rfiudcohr of t`ph ]@ buycs bhnstcntfs shn5 icncnb`c ofd rfiudcohr =.3, y t`fgph `ntfircd of 3 g`nuth. O`kuecr fd o`circgc of kdhqufs fn dczh bfrrcoh y bcdbudcr su junb`òn of trcnsjfrfnb`c. (=.:) ?) [czhncr s` fd s`stfgc fn dczh bfrrcoh fs fstckdf h nh.(=.2) 6) [czhncr bògh fs dc rfspufstc ofd s`stfgc fn dczh bfrrcoh cntf unc fntrcoc fn fsbcdòn un`tcr`h of dc rfjfrfnb`c, y bcdbudcr sus pcrãgftrhs. (=.2)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

2=

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

][HKDFGC ; (; ]VN_HR)  Bhnsòfrf fd s`stfgc of bhntrhd of dc Jìurc 3,ohnof [(s)7 , y I(s) fs dc junb`òn of trcnsjfrfnb`c ofd  s`stfgc buyc rfspufstc fsbcdòn fs dc of dc Jìurc ;. Jìurc 3

Jìurc ;

Rf pòf5 c) Acddcr I(s) (=. (=.6 6 punt hs). k) ]crc Lb73=, o`kuecr fd o`circgc of Khof cs`ntòt`bh (=.: ( =.: punths) punths ) quf df pfrg`tc fstuo`cr dc fstck`dòco fd s`stfgc of bhntrhd of dc jìurc 3. C pcrt`r of fsf o`circgc, oftfrg`nf of jhrgc cprhx`gcoc dhs vcdhrfs of dhs gãrifnfs of jcsf y icncnb`c ofd s`stfgc of bhntrhd (=.2 ( =.2 punths). punths ). Fn kcsf c dhs g`sghs, rczhnf dc fstck`dòco ofd s`stfgc of bhntrhd (=. (=.2 2 punths) punt hs) b) Fn fd bcsh of quf pcrc Lb73= fd s`stfgc fn dczh bfrrcoh rfsudtf fstckdf, bcdbudf fd frrhr fstcb`hncr`h cntf unc fntrcoc fsbcdòn of vcdhr 6. Fn fd bcsh of quf pcrc Lb73= fd s`stfgc fn dczh bfrrcoh sfc `nfstckdf, oftfrg`nf dhs vcdhrfs of Lb quf icrcnt`zcn dc fstck`dòco ofd g`sgh. (=. (=.2 2 punths) punths )

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

23

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 3 (3 ]VN_H) Ocoh fd s`stfgc buyc junb`òn of trcnsjfrfnb`c fs I



;s  2

s  2s ;  s  2

3.- ¸Fs phs`kdf rfoub`r su hrofn8 ¸]hr quà8 Fn bcsh of quf pufoc acbfrsf hktfnic dc junb`òn of trcnsjfrfnb`c ofd s`stfgc rfoubòh (=.6]ths). ;.- @no`quf buãd of dhs sìu`fntfs o`circgcs of Khof bhrrfsphnof bhn àd y eust`jçqufdh (=.6]ts). c)

k) O`circgc of Khof

O`circgc of Khof

=

6=

   )    K    o    (

  f    o   u    t    `   n   i   c    G

   )    K    o    (

-6=

-6= -3== -?6

-3== -326    )   i   f    o    (   f   s   c    a    ]

=

  f    o   u    t    `   n   i   c    G

   )   i   f    o    (   f   s   c    a    ]

-31= -;;6 -;9=

-0= -326 -31= -;;6

-;

3=

-3

=

3=

3

3=

;

3=

-3

3=

b)

3=

=

3=

3

3=

;

3=

o) O`circgc of Khof

O`circgc of Khof

=

;=

   )    K -;=    o    (   f    o -?=   u    t    `   n   i   c -:=    G

   )    K    o    (

-1= =    )   i   f    o    (   f   s   c    a    ]

-?= ?6

-?6

   )   i   f    o    (   f   s    a   c    ]

-0= -326 -31= -3 3=

=

  f    o   u    t    `   n -;=   i   c    G

=

3=

3

3=

;

3=

= -?6 -0= -326 -3

3=

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

=

3=

3

3=

;

3=

2;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN ; (3 ]VN_H) Cncd`zcr fd fjfbth quf dc vcr`cb`òn ofd pcrãgftrh _` (_`>=) prhoubf fn fd frrhr fstcb`hncr`h ofd s`stfgc of dc jìurc fn fd bcsh of fntrcocs t`ph (3) fsbcdòn (Y(s)73/s) y (;) rcgpc (Y(s)73/s ;). Rupònicsf quf fd s`stfgc I(s) pufof tfnfr (C)bfrh, (K)unh h (B)ohs phdhs fn fd hrìfn.

Fss, fjfbth _` fn Fss (C) R`stfgc s`n phdhs fn hrìfn+]@O   hrìfn+]@O (K) R`stfgc bhn un phdh fn fd

(3)Fntrcoc (3)Fntrcoc Fsbcdòn

(;)Fntrcoc (;)Fntrcoc [cgpc

hrìfn+]@O hrìfn+]@O (B) R`stfgc bhn ohs phdhs fn fd hrìfn+ ]@O ]@O

BVFR_@ÒN 2 (3 ]VN_H) Fn un rfiudcohr ]@O òfcd dc sfócd of bhntrhd sf fvcdõc c pcrt`r of dc sfócd of frrhr sfiõn dc jòrgudc5 t 3 o u (t )  L p (f(t )  f( )o   _o f(t )) _` = ot . Fn s`tucb`hnfs rfcdfs5



c) ¸Suà prhkdfgcs pufofn prfsfntcrsf ourcntf dc hpfrcb`òn of un rfiudcohr `gpdfgfntcoh bhn fstc jòrgudc8 (=.6]ths) k) ¸Bògh pufofn shdvfntcrsf fsths prhkdfgcs8 (=.6]ths)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

22

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n fxtrchro` fxtr chro` ncr`h (eud`h). (eud` h). Bursh 33-3; 33-3; ][HKDFGC (; ]VN_HR) () Vn surtòhr of icshd`nc pufof ghofdcrsf gfo`cntf dc fbucb`òn5 ; oS t  u (t )  ?¹S ; (t )  S(t ) . Ohnof S(t) fs ot fd bcuocd of icshd`nc quf oc fd surtòhr (d`trhs/sfiunoh) y u(t) fs dc tfns`òn of fntrcoc cd ghthr of dc khgkc ofd surtòhr (vhdt`hs), quf sf pufof gcn`pudcr c vhduntco. Rf bhnstruyf un s`stfgc of bhntrhd pcrc rfiudcr fd vhdugfn of icshd`nc sug`n`strcoc, Z(t). ]crc fddh sf

pdcntfc fd s`stfgc of bhntrhd of dc Jìurc 3. Fn o`bah fsqufgc fd vhdugfn of d`trhs ofsfcohs fs Z rfj . Rf sckf quf dc rfdcb`òn fntrf fd vhdugfn y fd bcuocd of icshd`nc sug`n`strcoh phr fd surtòhr v`fnf ocoh phr dc oZ (t )  S(t ) . sìu`fntf fbucb`òn o`jfrfnb`cd ot

Jìurc 3 c) Fdfiòh fd punth of trckceh S7=. d`trhs/sfiunoh, bcdbudf dc junb`òn of trcnsjfrfnb`c trcnsjfrfnb` c quf rfdcb`hnc fd vhdugfn of icshd`nc sug`n`strcoh phr fd surtòhr bhn dc tfns`òn of cd`gfntcb`òn of dc khgkc ofd surtòhr (I(s) fn dc jìurc 3). k) ]crc [(s)7L, fnbufntrf dhs vcdhrfs of L quf icrcnt`zcn dc fstck`dòco ofd s`stfgc of bhntrhd. b) ]crc fd rcnih of vcdhrfs of L fn dhs quf fd s`stfgc of bhntrhd fs fstckdf, rczhnf fd t`ph of rfspufstc ofd s`stfgc fn dczh bfrrcoh fn junb`òn of dhs vcdhrfs of L. o) ]crc L7=.=?6, rczhnf s` pufof rfoub`r fd hrofn of dc junb`òn of trcnsjfrfnb`c ofd s`stfgc fn dczh bfrrcoh. R` jufsf csç, rfouzbc o`bac junb`òn of trcnsjfrfnb`c f `no`quf dhs pcrãgftrhs bcrcbtfrçst`bhs of dc junb`òn of trcnsjfrfnb`c rfoubòc y o`kuef dc rfspufstc ofd s`stfgc cntf un fsbcdòn un`tcr`h.

][HKDFGC ; (; ]VN_HR) Ocoh fd s`stfgc rfcd`gfntcoh of dc jìurc5 + [   -

] V

;  

+

P

3

+

c) Bcdbudf dcs junb`hnfs of trcnsjfrfnb`c trcnsjfrfnb` c P( P(s s)/[( )/[(s s), P(s P(s)/]( )/](s s) y V(s V(s)/[( )/[(s s).(3 punth) k) Oftfrg`nf cprhx`gcocgfntf, pcrc L73, dhs gãrifnfs of jcsf y of icncnb`c ofd s`stfgc. (3 punth) b) Bcdbudf fd rcnih of vcdhrfs of L quf acbfn quf s`gudtãnfcgfnt s`gudtãnfcgfntf5 f5  Fd frrhr fstcb`hncr`h cntf unc fntrcoc rcgpc un`tcr`c fn [ sfc gfnhr quf =.3<  Cntf unc fntrcoc scdth tfnic un t`fgph of fstckdfb`g`fnth fstckdfb`g` fnth gfnhr quf ; (sfiunohs).

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

2?

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 3 (3 ]VN_H) Dcs sìu`fntfs irãj`bcs gufstrcn dc rfspufstc fn dczh bfrrcoh of buctrh s`stfgcs bhn rfcd`gfntcb`òn un`tcr`c of fntrcoc fntrcoc cpd`bcoc. nfict`vc. Fn bcoc irãj`bc sf `no`bc fd t`ph of Rf pòf5 c) C pcrt`r of dc rfspufstc ghstrcoc, ofoub`r fd t`ph ofd s`stfgc y s` acy frrhr fstcb`hncr`h, fstcb`hncr`h, h h nh. fstcb`hncr`h,, bcdbudcrdh. k) Fn bcsh of quf acyc frrhr fstcb`hncr`h

Rtfp [fsphnsf

D`nfcr R`gudct`hn [fsudts

=.3

36

=.=0 =.=1 =.=9 3= =.=:   f    o   u    t    `    d =.=6   p   g    C

  f    o   u    t    `    d   p   g    C

=.=?

6 =.=2 =.=; =.=3 =

=

=.3

=.;

=.2

=.?

=.6

=

=.:

=

6

3=

_`gf (sfb)

36

_`gf (sfb )

35 [fspufstc ofd R`stfgc 3 Jìurc 35 [fspufstc 3 cntf cntf fntrcoc scdth un`tcr`h

Jìurc 25 25 [fspufstc ofd R`stfgc 2 2 cntf cntf fntrcoc rcgpc un`tcr`c Rtfp [fsphnsf

D`nfcr R`gudct`hn [fsudts

:

3 =.0

6

=.1 =.9

?

=.:

  f    o   u    t    `    d 2   p   g    C

  f    o   u    t    ` =.6    d   p   g    C

=.? ;

=.2 =.;

3

=.3 =

=

=

3

;

2

?

6 _`gf (sfb)

:

9

1

0

3= 3=

Jìurc ;5 [fspufstc ofd R`stfgc ; cntf fntrcoc scdth un`tcr`h

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

=

=.6

3

3.6

;

;.6

_`gf (sfb)

Jìurc ?5 ?5 [fspufstc [fspufstc ofd s`stfgc ? ? cntf cntf fntrcoc scdth un`tcr`h

26

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN ; (3 ]VN_H) ]crc fd s`stfgc of dc jìurc acddcr5 c) Fbucb`òn bcrcbtfrçst`bc (=.96]ths), k) Zcdhr ofd pcrãgftrh pcrãgftrh —c‗ (c>=) of jhr jhrgc gc quf fd bhneunth tfnic cg cghrtìucg`fnth hrtìucg`fnth brçt`b brçt`bh h (=,6]ths), b) R` L sf jèc fn Lgcx, acddcr5 (3)rfspufstc fstcb`hncr`c ofd s`stfgc cntf un fsbcdòn unòco (bcsh of s`stfgc brçt`bcgfntf cghrtìucoh) y (;)t`fgph of fstckdfb`g`fnth (=.;6]ths).

BVFR_@ÒN 2 (3 ]VN_H) Bhnsòfrf un s`stfgc buyc rfspufstc fn jrfbufnb`c fs dc bhrrfsphno`fntf cd o`circgc of khof coeunth. c) Oftfrg`nf of jhrgc cprhx`gcoc fd cnbah of kcnoc ofd s`stfgc. k) Oftfrg`nf of jhrgc cprhx`gcoc dc icncnb`c fstãt`bc fn dcs unòcofs of dc junb`òn of trcnsjfrfnb`c trcnsjfrfnb` c ofd s`stfgc. b) R` o`bah s`stfgc fs fxb`tcoh bhn unc sfócd s`nushòcd of cgpd`tuo ;.6 y jrfbufnb`c =.2312 afrb`hs. ¸Buãd fs dc fxprfs`òn of dc scdòc ofd s`stfgc fn rài`gfn fstcb`hncr`h8

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

2:

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n hro` hr o`ncr`h ncr`h (eun`h). (eun `h). Bur Bursh sh 3;-32 3;-32 ][HKDFGC (2 ]VN_HR) Vn prhbfsh of sfbcoh (fd`g`ncb`òn of augfoco) cpd`bc un jdueh of c`rf bcd`fntf (gfo`cntf unc sfócd =…..3==% c un s`stfgc vfnt`dcohr), c dc bãgcrc of sfbcoh fn ohnof sf fnbufntrc fd gctfr`cd c sfbcr. Fstcnoh fn un punth of fqu`d`kr`h, sf rfcd`zc un fxpfr`gfnth bhns`stfntf fn o`sg`nu`r dc sfócd cd vfnt`dcohr un 3%, hksfrvãnohsf un bcgk`h fn dc augfoco ofd gctfr`cd bhgh fd ghstrcoh fn dc jìurc.

Rf pòf5 3. ]crc bhntrhdcr dc augfoco sf usc un bhntrhdcohr t`ph ]. O`kuecr un o`circgc of kdhqufs ofd s`stfgc of bhntrhd rfsudtcntf fn dczh bfrrcoh, fspfb`j`bcnoh dcs junb`hnfs of trcnsjfrfnb`c (=. (=.6 6 punths) punths ) ;. Bcdbudcr fd vcdhr of dc icncnb`c ofd rfiudcohr pcrc hktfnfr un shkrfp`bh ofd ;=% fn dc rfspufstc fn dczh bfrrcoh c un scdth of ohs unòcofs fn dc rfjfrfnb`c. (=. (=.: : punths) punths ) 2. Bcdbudcr fd vcdhr of of dc icncn icncnb`c b`c ofd rfiudco rfiudcohr hr pcrc hktfnfr hktfnfr un frrhr fstcb`hncr`h fstcb`hncr`h `njfr`hr cd cd =.3 % fn dc rfspufstc fn dczh bfrrcoh c un scdth ofd ;% fn dc rfjfrfnb`c (=.: punths). punths). ¸Buãd sfrã fd vcdhr fstcb`hncr`h of dc vcr`ckdf of scdòc y of dc vcr`ckdf gcn`pudcoc fn fstf bcsh8. ]crc fstc pcrtf rfbufroc bcdbudcr dcs o`st`ntcs junb`hnfs of trcnsjfrfnb`c ofd s`stfgc. P(s)/[(s) y V(s)/[(R) (=. (=.: : punths) punths ) ?. Bcdbudc fd gcrifn of jcsf y fd gcrifn of icncnb`c pcrc fd s`stfgc uscnoh fd rfiudcohr bcdbudcoh fn fd cpcrtcoh 2, rczhnc shkrf dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh (=. (=.9 9 punths) punths )

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

29

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 3 Ocoh fd o`circgc of kdhqufs of dc jìurc5

Rf pòf5 c) Fxprfscrdh fn dc jhrgc

k) R` A 3 s   ;, A ; s   3, I3 s   3, I ; s  

2s  ?

, I2 s   2, I? s  

3

s 3 s Bcdbudcr I(s), A(s) y Dc junb`òn of trcnsjfrfnb`c tr cnsjfrfnb`c fn dczh bfrrcoh b) Bhnsòfrcnoh dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh ofd cpcrtcoh k), ¸Buãd sfrçc fd t`fgph of fstckdfb`g`fnth fstckdfb`g`f nth s` sf cpd`bcsf unc fntrcoc fsbcdòn un`tcr`h cd s`stfgc8, ¸Acy shkrfp`bh8

BVFR_@ÒN ; Oftfrg`ncr buãd of dcs sìu`fntfs junb`hnfs of trcnsjfrfnb`c fs dc quf bhrrfsphnof bhn fd o`circgc of Khof. Eust`j`bcr dc rfspufstc.

I ( s) 

6=s  3= 

s  6=s  3

I( s) 

(c)

6=s  3=  ss  6=s  3 (k)

I( s) 

s  3= ss  6=s  3

I( s) 

(b)

6=3=s  3 ss  6=s  3 (o)

O`circgc of Khof

3==

6=    )    K    o    (    o   u    t    `

  n   i   c    G

=

-6=

-3== -0=

   )   i   f    o    (   f   s   c    J

-326

-31= -; 3=

-3

3=

=

3

3=

3=

;

3=

2

3=

Jrfbufnb`c (rco/s)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

21

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 2 Fd prhbfsh of dc jìurc rfprfsfntc un ahrnh of bcdfntcg`fnth of un gctfr`cd, quf fntrc c tfgpfrcturc _` y ofkf scd`r c tfgpfrcturc _. Fn fd ahrnh sf pufof gcn`pudcr fd jdueh J of fdfgfnth bcdfjcbthr pcrc acbfr quf dc tfgpfrcturc j`ncd _ ofd gctfr`cd cdbcnbf dhs vcdhrfs ofsfcohs. Rf sckf quf dc rfdcb`òn fntrf dc tfgpfrcturc _, dc tfgpfrcturc of fntrcoc ofd gctfr`cd _` y fd jdueh J v`fnf ococ phr5

6  2J 

o_

 ;_   ;  2J_  _ `

ot bhn _ y _` fn µB, J fn Li/g`n y fd t`fgph fn g`nuths, y quf bucnoh fd s`stfgc fstã fn fstcoh fstcb`hncr`h c ?=µB dc tfgpfrcturc of fntrcoc fs of 3=µB. Hktfnfr dc junb`òn of trcnsjfrfnb`c ofd s`stfgc fn fsf punth of trckceh, y o`kuecr fd o`circgc of kdhqufs, òfnt`j`bcnoh dc vcr`ckdf of fntrcoc, dc vcr`ckdf of scdòc y dc pfrturkcb`òn. BVFR_@ÒN ? Rfc un s`stfgc of dc jhrgc5

[(s) +

L

-

P(s)

I(s) A(s)

c) C pcrt`r ofshn dhs s`fgprf duicrfs of dcs rcçbfs of dcs rczhncr buãdfs t`fnfn junb`hnfs of trcnsjfrfnb`c fnof dczh bfrrcoh quf fstckdfs y buãdfs nh.jìurcs Cofgãs `no`bcr s` dc fstck`dòco sf prhoubf pcrc vcdhrfs dc icncnb`c L pfqufóhs h ircnofs. Eust`j`bcr dc rfspufstc. k) Fdfi`r unh of dhs duicrfs of dcs rcçbfs ghstrcohs fn dcs jìurcs y, suphn`fnoh A(s)73, ofoub`r dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh. [hht Dhbus

: H

?

   )

;

   3     s

   o   n   h   b   f   s    (   s    `   x    C   y   r   c   n    `   i   c   g    @

=

H

Q

Q

R`stfgc (3)

Q

-;

-? H

-: -3 ;

-3=

-1

-:

-? [fcd Cx`s (sfbhnos

=

;

)

[hht Dhbus

36

3=

-;

-3

H Q

   )

6

   3     s

   o   n   h   b   f   s    (   s    `   x    C   y   r   c   n    `   i   c   g    @

=

H

Q

H

R`stfgc (;)

Q

-6 Q

-3=

-36 - 3;

H

-3=

-1

-:

-?

-;

=

;

[fcd Cx`s (sfbhnos -3)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

20

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

[hht Dhbus

;= 36 3=    )

   3     s

6

  s    `   x    C   y   r   c   n    `

=

  i   c   g    @

-6

   o   n   h   b   f   s    (

Q

Q

Q Q

R`stfgc (2)

H

-3= -36 -;= - 2=

- ;6

- ;=

- 36

- 3= [fcd Cx`s (sfbhnos

-6

=

6

3=

-3

)

[hht Dhbus

2=

;=

   )

3=

Q

   3     s

   o   n   h   b   f   s    (   s    `   x    C   y   r   c   n    `   i   c   g    @

R`stfgc (?)

H

=

Q

Q H

-3=

Q

-;=

-2= - 3;

-3=

-1

-:

-?

-; [fcd Cx`s (sfbhnos

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

=

;

?

:

1

-3

)

?=

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n fxtrchro` fxtr chro` ncr`h (eud`h). (eud` h). Bursh 3;-32 3;-32 ][HKDFGC (2 ]VN_HR) Rf ofsfc bhntrhdcr dc _fgpfrcturc of un rfcbthr quçg`bh fxhtàrg`bh (fd prhbfsh cshb`coh ofsprfnof bcdhr quf acy quf o`s`pcr), ut`d`zcnoh bhgh cbtucohr unc vãdvudc of rfiudcb`òn phr ohnof b`rbudc fd dçquòh rfjrìfrcntf (quf jcvhrfbf dc fd`g`ncb`òn ofd bcdhr prhoubòh fn fd prhbfsh). Fn un fnscyh fn Dczh Ck`frth sf ac gfoòh dc rfspufstc tfgphrcd ofd rfcbthr (_fgpfrcturc fn µB of dc rfcbb`òn fn fefbub`òn) bucnoh dc sfócd vãdvudc rfspfbth of su punth of trckceh. Dc _fgpfrcturc rfi`strcoc pufof cpd`bcoc vfrsf fn cdc dc jìurc (fef vcr`ckc tfgphrcdfn fn-;=% g`nuths).

3 ;

=.6 punths =.6 punths

2

3.6 punths

?

Acddcr dc Junb`òn of _rcnsjfrfnb`c ofd R`stfgc (vãdvudc-rfcbthr) (vãdvudc-rfcbt hr) R` dc sfócd cpd`bcoc c dc vãdvudc fs sfnhòcd of pfr`hoh 6 g`n y cgpd`tuo ;.6% ¸Bògh fs dc rfspufstc ofd s`stfgc fn fstcoh fstcb`hncr`h8 (cgpd`tuo, jrfbufnb`c y ofsjcsf)

O`sfócr un [fiudcohr of tcd sufrtf quf fd s`stfgc (rfiudcohr vãdvudc rfcbthr) fn Dczh Bfrrcoh y bhn rfcd`gfntcb`òn unòco (3) Nh prfsfntf frrhr fstcb`hncr`h jrfntf c bcgk`hs fsbcdòn fn dc bhnsìnc, (;) nh prfsfntf shkrfp`bh cntf dhs g`sghs bcgk`hs y (2) quf sf fstck`d`bf fn un t`fgph nh supfr`hr c 2 g`nuths. Eust`j`bcr dc fdfbb`òn ofd [fiudcohr fgpdfcoh f `no`bcr fd vcdhr of sus pcrãgftrhs. =.6 punths R` dc bhnsìnc h rfjfrfnb`c vcrçc sfiõn unc rcgpc of pfno`fntf 6 µB /g`n. ¸]rfsfntcrã fd s`stfgc frrhr fstcb`hncr`h8. Fn bcsh cj`rgct`vh bcdbudcrdh

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

?3

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN BVFR_ @ÒN 3 (; (; punths pun ths ) Rf o`sphnf of un s`stfgc fn dczh bfrrcoh bhn dc bhnjìurcb`òn quf sf gufstrc fn dc jìurc

Y(s) +

-

B(s )

I

Ib

Ohnof

I( s) 

? s ;  3?s  ;?

Rf pòf5 C

=.96p

K

=.6p

B

=.96p

Bcrcbtfrçst`bcs of dc rfspufstc tfgphrcd (trcns`thr`c y pfrgcnf pfrgcnfntf) ntf) ofd s`stfgc fn DB cntf unc fntrcoc fsbcdòn pcrc dhs bcshs fn quf Ib(s) sfc un rfiudcohr prhphrb`hncd bhn Lp73 h Lp7??.36 Bhgpcrcr y bhgfntcr dhs rfsudtcohs. _rczcr fd Duicr of dcs rcçbfs —cprhx`gcoh‗ pcrc fd s`stfgc bhn Ib(s)7L, bhn L>=. Bhgfntcr dhs rfsudtcohs. rfsudtcohs. Bcdbudcr dhs GJ y GI —cprhx`gcohs‗ pcrc fd s`stfgc bhn Ib(s)73 y pcrc fd s`stfgc bhn Ib(s)7??.36

BVFR_@ÒN BVFR_ @ÒN ; (3 punth) punt h) Rfc

un

I s  

s`stfgc

bhgh

fd

of

;=

s

;

 9 s  3; s ;  ; s  ; 

dc

jìurc,

ohnof

V(s ) V(s)

I

B(s) B(s )

Rf cpd`bc bhgh fntrcoc unc rcgpc un`tcr`c. Rf pòf5 c) Hktfnfr dc ofsbhgphs`b`òn ofsbhgphs`b` òn fn jrcbb`hnfs s`gpdfs of dc scdòc ofd s`stfgc, sfócdcnoh y eust`j`bcnoh eust`j` bcnoh quà tàrg`nhs bhrrfsphnofn c dc rfspufstc trcns`thr`c y bucdfs c dc pfrgcnfntf. (Bhgfntcr`h5 nh fs nfbfscr`h acbfr dhs bãdbudhs nugàr`bhs) k) R` fd nugfrcohr of I(s) jufrc 6=, ¸sf vfrçc cjfbtcoh fd ofscrrhddh of cdiunc jhrgc8

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

?;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN BVFR_ @ÒN 2 (3 punth) punt h) 3. Ocoh fd s`stfgc bhn rfcd`gfntcb`òn un`tcr`c of dc jìurc, su o`circgc of Khof (J_ fn dczh ck`frth) fs fd quf sf gufstrc. Hktfnic dhs gãrifnfs of jcsf y of icncnb`c.

I s  

;=== ( s  =.3)

s  :s  ;s  3=

Y(s) +

I

-

Ibs   3 

;. Rf df cpd`bc un bhntrhdcohr ]@

Y(s) +

3

B(s)

I

Ib

3=s

B(s )

-

Hktfnic fd nufvh o`circgc of Khof y dhs nufvhs gãrifnfs of jcsf y icncnb`c. ¸Buãd fs dc pr`nb`pcd vfntcec ofd s`stfgc bhgpfnscoh8

?= 2= ;= 3= ?.? = -3= -;= -2= -?= -6= -:= -2 3=

-;

3=

-3

3=

3=

=

3=

3

;

3=

3=

2

3== 6= = -6= -3== -36= -;== -2 3=

-;

3=

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

-3

3=

=

3=

3

3=

2

;

3=

3=

?2

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n hro` hr o`ncr`h ncr`h (eun`h). (eun `h). Bur Bursh sh 32-3? 32-3? ]rhkdfgc (2 punths) Dc prfs`òn of un ofpòs`th of cdgcbfncg`fnth of un b`frth ics sf rfiudc phr gfo`h of un s`stfgc bhgh fd of dc jìurc, gcn`pudcnoh dc dçnfc of scdòc, ohnof ]_ fs fd sfnshr of prfs`òn, ]B fs fd rfiudcohr of prfs`òn, y _ fs dc tfgpfrcturc of fntrcoc ofd ics. Fd s`stfgc hpfrc nhrgcdgfntf c unc prfs`òn of 2 kcrfs fn fd ofpòs`th of cdgcbfncg`fnth y bhn unc sfócd of dc vãdvudc ofd 2=% (ohnof fd rcnih of junb`hncg`fnth of dc vãdvudc fs fntrf fd = y fd 3==%). Rf sckf quf fd s`stfgc, fn dczh ck`frth, cntf un bcgk`h fn dc sfócd of dc vãdvudc ofsof fd 2= % cd 26% oc unc rfspufstc tfgphrcd fn dc prfs`òn bhgh dc of dc jìurc5 Rtfp [fsphnsf

2 ;.0 ;.1 ;.9 ;.:

  f    o    t   u    `    d   p   g    C

;.6 ;.? ;.2 ;.; ;.3 ; =

3

;

2

?

6

:

_`gf (sfb)

9

1

0

3=

33

3;

Rf sckf cofgãs quf dc rfdcb`òn fntrf dc tfgpfrcturc _ (fn µB) ofd ics quf ddfic cd ofpòs`th of cdgcbfncg`fnth y dc prfs`òn ofntrh g`sgh (fn kcrfs), pcrc unc cpfrturc of dc vãdvudc ofd 2=% y unc prfs`òn of 2 kcrfs, v`fnf ococ phr dc sìu`fntf fbucb`òn5 op

;

31== ot   2 p(t )

 2=_ (t )  2=

Rf pòf5 c) O`kuef fd bhrrfsphno`fntf bhrrfsphno`fntf o`circgc of kdhqufs fn dczh ck`frth, `no`bcno `no`bcnoh h bucd fs dc vcr`ckdf bhntrhdcoc, dc vcr`ckdf gcn`pudcoc y dc vcr`ckdf of pfrturkcb`òn, bcdbudcnoh dcs bhrrfsphno`fntfs junb`hnfs of trcnsjfrfnb`c. k) O`sfóf un rfiudcohr pcrc fstc pdcntc quf quf prfsfntf fn dczh bfrrcoh un frrhr fstcb`hncr`h of =.3 cntf un scdth fn fd vcdhr ofsfcoh of dc prfs`òn of ; unòcofs. O`kuef fd bhrrfsphno`fntf o`circgc of kdhqufs fn dczh bfrrcoh b) ¸Bògh sfrã fd vcdhr ofd frrhr, of dc scdòc (]) y of dc sfócd of bhnthd (V) fn fd fstcb`hncr`h ofd s`stfgc fn dczh bfrrcoh bucnoh dc tfgpfrcturc of fntrcoc vcrçf 3= unòcofs8 o) Bcdbudc fd gcrifn of jcsf y fd gcrifn of icncnb`c of fstf s`stfgc bhn fd bhntrhdcohr bcdbudcoh fn fd cpcrtcoh k), bhgfntc bhn fsths vcdhrfs bhgh fs dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh. ]ufof sfr õt`d acbfr fd trczcoh cprhx`gcoh ofd o`circgc of Khof. Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3: Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

??

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 3 (3 ]VN_H). Cd shgftfr c un s`stfgc fn dczh bfrrcoh y bhn rfcd`gfntcb`òn rfcd`gfntcb`òn un`tcr`c c unc fntrcoc fsbcdòn un`tcr`h fn dc rfjfrfnb`c, sf hkt`fnf dc sìu`fntf rfspufstc5

y (t )  ;=  3.33f

 t

 ;3.33f =.3t

c) Hktfnic dc junb`òn of trcnsjfrfnb`c fn dczh bfrrcoh of fsf s`stfgc y fd vcdhr of dc icncnb`c. k) ¸Fs fstckdf h nh8 ¸]hr quà8 Fn bcsh sfr fs8 fstckdf hktfnic fd frrhr fstcb`hncr`h y fd t`ph. b) ¸Of o) quàof hrofn Acic un trczcoh cprhx`gcoh of dc rfspufstc ofd s`stfgc y eust`jçqufdh. BVFR_@ÒN ; (3.6 ]VN_HR). Rf o`sphnf of un s`stfgc bhgh sf gufstrc fn dc jìurc

I( s ) 

s  6 ( s  3)( s  c )

Rf pòf5 c) R` [(s)7L (L>= ) trczcr fd duicr of dcs rcçbfs cprhx`gcoh s` c>6. k) Fstuo`cr dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh. Bògh fs dc rfspufstc ofd s`stfgc fn dczh bfrrcoh cntf un fsbcdòn un`tcr`h. Frrhr fn fstcoh fstcb`hncr`h cntf fntrcoc fsbcdòn, cntf fntrcoc rcgpc y cntf fntrcoc pcrãkhdc. b) Gcntfn`fnoh c>6, fdfi`r dc rfdcb`òn fntrf L   ( L>= ) y c quf icrcnt`bf un frrhr fstcb`hncr`h (cntf fntrcoc fsbcdòn un`tcr`h) gfnhr ofd 3=%.

o) [fpft`r fd cpcrtcoh k ) s` [( s )  Duicr of dcs [cçbfs.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

L ( s  c ) s

( L>= ). ). ]ufof sfr õt`d acbfr un trczcoh cprhx`gcoh ofd

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

?6

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

BVFR_@ÒN 2 (3.6 ]VN_HR). Dc jìurc 3 gufstrc fd ghofdh s`gpd`j`bcoh of unc vìc ahr`zhntcd fn vhdco`zh (fgphtrcoc phr un fxtrfgh y d`krf fn fd htrh) c dc bucd sf df ac bhdhbcoh bhdhbcoh pròx`gh cd fxtrfgh d`krf un cbtucohr cbtucohr fdfbtrhgcinàt`bh fdfbtrhgcinàt`bh (s`n bhntcbth) quf ifnfrc unc jufrzc J(t) vfrt`bcd fn junb`òn of dc tfns`òn cpd`bcoc Z(t) shkrf fd fxtrfgh d`krf b`tcoh. Csç g`sgh shkrf dc vìc pufof cbtucr htrc jufrzc fxtfrnc vfrt`bcd O(t) nh ofsfcoc (pfrturkcb`òn) buyh fjfbth sf ofkf g`tìcr bhn fd b`tcoh cbtucohr.

Jìurc 3 Rf pòf5 c) ¸Buãd fs fd fjfbth of dc jufrzc fxtfrnc O(t) shkrf dc scdòc P(s), fn rài`gfn fstcb`hncr`h, s` o`bac jufrzc O(t) jufrc sfnhòcd of jrfbufnb`c j(Az) y cgpd`tuo C(N)8 ¸Buãd fs dc fxprfs`òn cncdçt`bc of dc scdòc y(t) fn rài`gfn fstcb`hncr`h fn fstf bcsh8 k) ¸Bckf fspfrcr cdiõn fjfbth nh ofsfcoh quf pufoc sfr pfreuo`b`cd pcrc fd s`stfgc8 ¸C quà jrfbufnb`c (Az) sfrçc phs`kdf8 ¸Buãd sfrã dc cgpd`j`bcb`òn8 cgpd`j`bcb`òn8 sf b`frrc fd dczh (jìurc ;) gò`fnoh dc scdòc P(s) y fgpdfcn fgpdfcnoh oh un bhntrhdcohr (3)[(s)7L h b) R` (;)[(s)7L(3+3/s_`), ¸Buãd sfrçc fd fjfbth of dc pfrturkcb`òn shkrf dc scdòc fstcb`hncr`c s` dc pfrturkcb`òn jufrc fsbcdòn, fn duicr of sfnhòcd, of vcdhr O fn bcoc bcsh8

Jìurc ;

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

?:

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n fxtrchr o` o`ncr`h ncr`h (eud`h). (eud` h). Bursh 32-3? 32-3? ]rhkdfgc 3 (3.1 punt hs. Cpcrtcoh Cp crtcoh c) =.1p, =.1p, cpcrtcoh k) 3p) Fn dc Jìurc pufof vfrsf un o`sphs`t`vh fn fd quf un prhoubth coqu`frf unc v`sbhsòco Z t rcs sfr prhbfscoh. Rf bhnhbf quf dc rfdcb`òn fntrf dc v`sbhsòco Z , dc tfgpfrcturc _   of fntrcoc ofd prhoubth y dc sfócd u cd ghthr G v`fnf ococ phr5

Z

oZ ot

 Z_  ku(t )

Dc tfgpfrcturc _   v`fnf `gpufstc phr fd prhbfsh cntfr`hr g`fntrcs quf dc sfócd u pufof sfr gcn`pudcoc. Rf sckf tcgk`àn quf fd s`stfgc hpfrc nhrgcdgfntf bhn un vcdhr of u fn thrnh cd 2=% of su rcnih, vcdhr pcrc fd bucd, fn bhno`b`hnfs fstcb`hncr`cs y bhn unc tfgpfrcturc of fntrcoc of :=µB, dc v`sbhsòco vcdf 6=. Rf pòf5 c) @no`bcr buãd fs dc vcr`ckdf gcn`pudcoc, dc pfrturkcb`òn y dc vcr`ckdf bhntrhdcoc. O`kuecr fd bhrrfsphno`fntf o`circgc of kdhqufs fn dczh ck`frth `no`bcnoh dcs junb`hnfs of trcnsjfrfnb`c. k) Bfrrcr fd dczh of bhntrhd bhn un rfiudcohr of dc v`sbhsòco of scdòc bhn fd br`tfr`h of hktfnfr unc rfspufstc cntf bcgk`hs fn dc rfjfrfnb`c fn scdth s`n frrhr fstcb`hncr`h, quf nh tfnic shkrfp`bh y bhn fd quf fd t`fgph of csfntcg`fnth sfc ìucd c ; g`nuths. O`kuec fd bhrrfsphno`fntf o`circgc of kdhqufs fn dczh bfrrcoh.

]rhkdfgc ; (;punths. Bcoc cpcrtcoh cpcrtcoh =.6 punths) punth s) Ocoh fd s`stfgc fn dczh bfrrcoh of dc jìurc fn fd quf

I( s ) 

3= 6s  :

y O( s) 

6 , sf pòf5 6s  :

c) Bcdbudcr fd vcdhr ofd frrhr frrhr y of dc sfócd of bhntrhd fn fd fd fstcb`hncr`h s` acy acy un scdth fn dc rfjfrfnb`c rfjfrfnb`c of ; 3   unòcofs, fn ohs bcshs, bucnoh [(s)73.? y bucnoh [( s )  3.?3   = . 9 s   k) Bcdbudcr fd vcdhr vcdhr ofd frrhr y of dc sfócd of of bhntrhd fn fd fstcb`hncr`h fstcb`hncr`h s` Z(s) bcgk`c bhnt`nucgfntf c rczòn of 3   ; unòcofs phr sfiunoh, fn cgkhs bcshs, fs ofb`r, bucnoh [(s)73.? y bucnoh [( s)  3.?3  

  =.;9 ssfiunohs, b) R` dc bhnsìnc ofd s`stfgc fxpfr`gfntc bcgk`hs s`nushòcdfs of cgpd`tuo ; unòcofs y pfr`hoh ¸Buãd sfrã dc fvhdub`òn of dc scdòc cd bckh of un b`frth t`fgph8 o) O`kuec fd duicr duicr of dcs rcçbfs of fstf s`stfgc, bucnoh bucnoh fd rfiudcohr rfiudcohr [(s) bcdbudcoh fs un ]@, bhn vcdhr of _`73.; . Bhgfntc bhgh fs dc fstck`dòco ofd s`stfgc fn dczh bfrrcoh, y bhgh fs dc rfspufstc ofd s`stfgc fn dczh bfrrcoh pcrc o`st`nths vcdhrfs of Lp.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

?9

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Bufst`òn 3 (3.; (3.; punths. punt hs. Cpcrtcoh Cp crtcoh c) =.?p, =.?p, cpcrtcoh k) =.;p, cpcrtcoh b) =.:p ) Rf o`sphnf of un s`stfgc bhgh sf gufstrc fn dc jìurc. ]crc [(s)73 sf ac hktfnòh fd o`circgc of Khof of dc J_ fn Dczh Ck`frth quf sf gufstrc

Khof O`circg

;= 3=    )    K    o    (   f    o   u    t    `   n   i   c    G

= -3= -;= -2= -?= -6= =

   )   i   f    o    (   f   s   c    a    ]

-?6

-0= -; 3=

-3

3=

3=

=

3

3=

3=

;

3=

2

Jrfqufnby (rco/s)

Rf pòf5 c) C buãd of dcs sìu`fntfs sìu`fntfs J_ bhrrfsphnof bhrrfsphnof fd o`circgc (eust`j`bcr dc rfspufstc) rfspufstc)

I( s) 

s  6 s ;  33s  3=

I( s) 

3=s s ;  33s  3=

I( s ) 

:s  6 s ;  33s  3=

I ( s) 

:s  3 s;

 33s  3=

(c) (k) (b) (o) k) ]crc dc J_ fdfiòc fn fd cpcrtcoh cntfr`hr, y uscnoh fd o`circgc of Khof, ofb`r buãdfs shn dhs Gãrifnfs of Jcsf y of Icncnb`c. b) ]crc dc J_ fdfiòc fn fd cpcrtcoh 3 y s` [(s)7L , fdfi`r un vcdhr of L   quf icrcnt`bf un gcrifn of jcsf of cd gfnhs 3?=µ (fgpdfcr fd khof of dc jìurc bhgh cyuoc).

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

?1

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Bufst`òn ; (=.1 (=.1 punths. punth s. Cpcrtcoh Cp crtcoh c) =.?p, =.?p, cpcrtcoh k) =.?p) Vn s`stfgc buyc junb`òn of trcnsjfrfnb`c of dczh bfrrcoh fs J ( s) 

P ( s)

C

prfsfntc unc rfspufstc  Ks;  Bs  O Y ( s)

cntf un fsbcdòn un`tcr`h bhgh dc quf cpcrfbf fn dc sìu`fntf jìurc. jìurc. Rtfp [fsphnsf

=.9

=.:

=.6

  f    o   u    t    `    d   p   g    C

=.?

=.2

=.;

=.3

= =

3

;

2

? _`gf (sfbhnos)

Rf pòf c) Hktfnfr dhs vcdhrfs of C,K,B y O. k) hktfnic R` fstf s`stfgc t`fnfoffd dcsìu`fntf of kdhqufs, dc fxprfs`òn junb`òn o`circgc of trcnsjfrfnb`c I fn junb`òn of J .

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

?.9

6

:

9

1

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

?0

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Bufst`òn 2 (3.; (3.; punt hs. Cpcrtcoh C pcrtcoh c) =.2p, cpcrtcoh cpcrtcoh k) =.2p, cpcrtcoh cpcrtcoh b) =.2p, cpcrtcoh cpcrtcoh o) =.2p) ]crc dhs sìu`fntfs s`stfgcs, bhntfstcr dcs prfiuntcs quf sf `no`bcn fn bcoc cpcrtcoh5 c) Vn s`stfgc bhn icncnb`c vcr`ckdf buyh duicr [hht Dhbus ifhgàtr`bh of dcs rcçbfs sf rfprfsfntc fn dc 36 jìurc. Oftfrg`nc s` fs fstckdf, kceh quà bhno`b`hnfs y phr quà. Fxpd`bc bògh sfrçc dc 3= jhrgc of su rfspufstc tfgphrcd (irhssh ghoh) cntf unc fntrcoc fn fsbcdòn fn dczh 6   s    `   x    C   y   r   c   n    `   i   c   g    @

bfrrcoh icncnb`c).(pcrc o`jfrfntfs vcdhrfs of dc

= -6 -3= -36 - ;6

-;=

- 36

- 3= [fcd Cx`s

-6

=

6

k) Vn s`stfgc o`nãg`bh buyc scdòc fs dc vcr`ckdf vcr`ckdf y(t), buyc fntrcoc fs u(t) y quf fstã ofsbr`th phr dc sìu`fntf fbucb`òn o`jfrfnb`cd5 y' ' (t )  ;.: y ' (t )  2 y (t )  39.?2u(t ) .

Oftfrg`nc s` fs fstckdf, kceh quà bhno`b`hnfs y phr quà. Fxpd`bc bògh sfrçc su rfspufstc tfgphrcd (irhssh ghoh) cntf unc fntrcoc fn fsbcdòn fn dc vcr`ckdf u(t)s ` dhs vcdhrfs of y, y‐ f y‐‐ f n fd fstcoh `n`b`cd shn bfrh. b) Vn s`stfgc s`stfgc bhn rfcd`gfntcb`òn rfcd`gfntcb`òn un`tc un`tcr`c r`c buyc junb`òn of trcnsjfrfnb`c fn dczh prfsfntc fd o`circgc of Khof of dcck`frth jìurc Oftfrg`nc s` fs fstckdf, kceh quà bhno`b`hnfss y phr quà. bhno`b`hnf

o) junb`òn Vn s`stfgc s`stfgc rfcd`gfntcb`òn rfcd`gfntcb`ò un`tc un`tcr`c r`c buyc of bhn trcnsjfrfnb`c fnn dczh bfrrcoh prfsfntc fd o`circgc of Khof of dc jìurc. Oftfrg`nc s` fs fstckdf, kceh quà bhno`b`hnfs y phr quà.

Khof O`circg ;=    ) 3=    K    o    (   f    o =   u    t    `   n   i   c    G -3=

-;= =    )   i   f    o    (   f   s   c    a    ]

-?6

-0= -; 3=

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

-3

3=

=

3= Jrfqufnby (rco/sfb)

3

3=

;

3=

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

6=

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n hro` hr o`ncr` ncr`h h (eun`h). (eun `h). Bur Bursh sh 3?-36 3?-36 ]rhkdfgc 2 punths Vn s`stfgc of bhntrhd ofd i`rh of un ghthr sf bhntrhdc gfo`cntf un bhntrhd prhphrb`hncd of icncnb`c 3 y rfcd`gfntcb`òn un`tcr`c. ]crc unc rfjfrfnb`c cniudcr fsbcdòn of Y73 rco . dc scdòc P   ofd s`stfgc fs dc of dc jìurc5 Rtfp [fsphnsf

3.? 3.; 3   f    o   u    t    `    d   p   g    C

=.1 =.: =.? =.; = =

3

;

2

?

6

:

9

1

_`gf (sfbhnos)

Y(s) +

V(s)

F(s)

-

3

P(s) I(s)

Rf pòf5 3. Dc junb`òn of trcnsjfrfnb`c I ofd ofd s`stfgc (ãniu (ãniudh dh i`rcoh jrfntf c tfns`òn of cd`gfntcb`òn cd`gfntcb`òn cd ghthr). ghthr). ;. Fstuo`f dc fstck`dòco ofd ofd s`stfgc gfo`cntf fd o`circgc of Khof fn junb`ò junb`òn n ofd vcdhr ofd bhntrhdcohr prhphrb`hncd. 2. Hktfnic fd frrhr fstcb`hncr`h fstcb`hncr`h quf tfnorçc fd s`stfgc cntf unc fntrcoc fntrcoc rcgpc



; s

?. Rf bcgk`c fd bhntrhdcohr bhntrhdcohr prhphrb`hncd prhphrb`hncd phr un bhntrhdcohr bhntrhdcohr ]@ of dc jhrgc5 L 3  



;

3 

.

_ ` s 

O`kuef fd DO[ ofd s`stfgc y fstuo`f su fstck`dòco fn junb`òn of L , pcrc vcdhrfs of _`7; y _`7 =.:;3. =.:;3. 2.336 . O`sfóf un bhntrhdcohr quf acic quf fd 6. Ruphnic un s`stfgc bhn rfcd`gfntcb`òn rfcd`gfntcb `òn un`tcr`c y I  s  3 .6 s`stfgc fn dczh bfrrcoh tfnic cntf unc fntrcoc fsbcdòn un`tcr`h fn dc rfjfrfnb`c, frrhr fstcb`hncr`h nudh, shkrf`gpudsh gãx`gh ofd 6% y t`fgph of p`bh of 3s.

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

63

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c. B3

Fnunb`cohs ]rãbt`bcs Cud Cudc c

3.; pun th

]crt`fnoh of dc fstrubturc ifnàr`bc of un s`stfgc bhn rfcd`gfntcb`òn un`tcr`c. c) [czhncr pcrc bcoc unh of dhs duicrf duicrfs s of dcs rcçbfs sìu`fntfs s` fd s`stfgc fn dczh bfrrcoh sfrã s`fgprf fstckdf h nh. k) Eust`j`bcr s` cdiu cdiunc nc of dcs junb`hnfs of trcnsjfrfnb`c fn dczh ck`frth sìu`fntfs bhrrfsphnof c cdiunh of dhs irãj`bhs. ;

3 ; s  3

3 ? s  3

[hhtDhbus

;

  s    `   x    C   y   r   c   n    `   i   c   g    @

3.6

3.6

3

3

=

=.6

   )   s    o   n   h   b   f   s    (

   3   -

x

  s    `   x    C   y   r   c   n    `   i   c   g    @

-=.6

-=.6 -3

-3.6

-3.6

-3

-=.1

-=.:

-=.?

-=.;

=

x

=

-3

-; -3.;

[hhtDhbus

;

=.6

   )   s    o   n   h   b   f   s    (

   3   -

s  3=s  ;=2s  3=3 s  =.6

-; -2.6

=.;

-2

-;.6

-;

-3.6

(c)

   )   s    o   n   h   b   f   s    (

  s    `   x    C   y   r   c   n    `   i   c   g    @

1

=.1

:

=.:

; = -;

=.6

3

=.?    )   s    o   n   h   b   f   s    (

   3   -

h h h

x

  s    `   x    C   y   r   c   n    `   i   c   g    @

=.;

-=.?

-:

-=.:

-1

-=.1 -3=

-1

-:

-?

-;

[fcdCx`s (sfbhnos -3)

(b)

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

=

x

=

x

h

-=.;

-?

-3= -3;

=

[hhtDhbus

3

?    3   -

-=.6

(k)

[hhtDhbus

3=

-3

[fcdCx`s (sfbhnos-3)

[fcdCx`s (sfbhnos-3)

-3 -3?

-3;

-3=

-1

-:

-?

-;

[fcdCx`s (sfbhnos-3)

(o)

=

;

?

:

1

Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

6;

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c. B;

Fnunb`cohs ]rãbt`bcs Cud Cudc c

3.; pun th

Rf cpd`bc unc sfócd fsbcdòn un`tcr`h fn fd `nstcntf = c b`nbh s`stfgcs o`jfrfntfs c), k), b), o) y f), hktfn`ànohsf dcs irãj`bcs 3, ;, 2, ? y 6. Fgpcrfef bcoc irãj`bc bhn fd s`stfgc bhrrfsphno`fntf y eust`j`quf su rfspufstc.

(c)

(k)

(b)

(o)

(f)

Rtfp [fsphnsf

=.;6

Rtfp [fsphnsf

=.;6 =.;

=.;

=.36

=.36   f    o   u    t    `    d   p   g    C

  f    o   u    t    `    d   p   g    C

=.3

=.3

=.=6

=.=6

= =

=.6

3

3.6

;

;.6

2

2.6

?

?.6

= =

6

=.6

3

3.6

;

(3)

2

2.6

2

2.6

?

?.6

6

(;)

Rtfp[fsphnsf

=.;6

;.6 _`gf (sfbhnos)

_`gf (sfbhnos)

Rtfp [fsphnsf

;

=.;

3.6

=.36   f    o   u    t    `    d   p   g    C

  f    o   u    t    `    d   p   g    C

=.3

=.6

=.=6 = =

3

=.6

3

3.6

;

;.6

2

2.6

?

?.6

= =

6

_`gf (sfbhnos)

=.6

3

3.6

;

;.6 _`gf (sfbhnos)

(2)

(?) Rtfp [fsphnsf

=.26 =.2 =.;6   f    o   u    t    `    d   p   g    C

=.; =.36 =.3 =.=6 = =

=.6

3

3.6

;

;.6 _`gf (sfbhnos)

6

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

2

2.6

?

?.6

6

?

?.6

6

Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

62

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c. B2

Fnunb`cohs ]rãbt`bcs Cud Cudc c

3.: pun punths ths

Rf o`sphnf of un ofpòs`th bòn`bh bhgh fd of dc jìurc, fn fd quf fd vhdugfn ofd dçquòh bhntfnòh fs prhphrb`hncd, bhn dc bhnstcntf l , cd bukh of dc cdturc a ofd dçquòh fn fd ofpòs`th. Fd ofpòs`th sf ddfnc bhn un bcuocd q f y sf vcbçc bhn htrh bcuocd q s . Fd ghofdh quf ofsbr`kf dc o`nãg`bc ofd s`stfgc fstã ofsbr`th phr dcs sìu`fntfs fbucb`hnfs5 fbucb`hnfs5 oZ (t ) f s ot  q (t )  q (t ) Z (t )  la 2 (t ) q s (t )  BR ; ia(t )  K a(t )

qf

a

Z

qv

Ohnof, B 7 bhfj`b`fntf of bhntrcbb`òn of vfnc (co`gfns`hncd), (co`gfns`hncd), R 7 ãrfc ofd hr`j`b`h of scdòc (g ;), K7=.==3, l7; , (unòcofs R@). Rf pcrtf of unc s`tucb`òn of fqu`d`kr`h fn dc quf fd bcuocd of fntrcoc fs of =.=3g2/s y sf pòf5 c) Hktfnfr dc junb`òn of trcnsjfrfnb`c trcnsjfrfn b`c fntrf a y qf y dc junb`òn of trcnsjfrfnb`c fntrf qs y qf. k) R` fn fd `nstcntf t7= fd bcuocd bcuocd of ddfncoh q ddfncoh qf cugfntc krusbcgfntf acstc =.=; g2/s, `no`bcr fd t`fgph quf tcroc fd n`vfd fn cdbcnzcr su nufvh fstcoh fstcb`hncr`h y buãd fs su vcdhr. b) ¸Buãd fs fd frrhr quf sf ac bhgftòh bhn dc d`nfcd`zcb`òn8

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Fnunb`cohs Fnunb` cohs ]rãbt`bcs Cudc

6?

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

Fxcgfn Fxcgf n fxtrchr o` o`ncr`h ncr`h (eud`h). (eud` h). Bursh 3?-36 3?-36 BVFR_@HNFR B3.. (3.; p) B3 p)O coh un s`stfgc bhn junb`òn of trcnsjfrfnb`c I ( s) 

; s

;

 6s  :

. Rf pòf5

3. (=.? p) p) Bhgprhkcr s` fs un s`stfgc sukcghrtìucoh, shkrfcghrtìucoh h brçt`bcgfntf cghrtìucoh. ;. (=.1 p) R` sf p) R` b`frrc fd dczh bhnsfrã unc fd rfcd`gfntcb`òn of icncnb`c ; y un of vcdhr L>=, `no`bcr bògh bhgphrtcg`fnth ofd s`stfgc fn bhntrhdcohr junb`òn ofdprhphrb`hncd vcdhr of L. Hktfnfr tcgk`àn fd vcdhr ofd frrhr fstcb`hncr`h cntf unc fntrcoc fsbcdòn fn junb`òn of fsf vcdhr of L. B;. (3.; punth) Rfc un s`stfgc bhn rfcd`gfntcb`òn un`tcr`c nfict`vc, tcd quf su o`circgc of Khof fn dczh ck`frth ([I) v`fnf ocoh phr dc jìurc sìu`fntf5 Khof O`circg

1=

:=

   )    K    o    (   f    o   u    t    `   n   i   c    G

?=

;=

=

-;= ?6

=    )   i   f    o    (

  f   s   c    a    ]

-?6

-0=

-326 -2 3=

-;

-3

3=

=

3=

3=

3

;

3=

3=

2

3=

Jrfqufnby (rco/sfb)

[czhncr s` dcs cj`rgcb`hnfs sìu`fntfs shn b`frtcs h jcdscs. c) Fd s`stfgc fn dczh bfrrcoh nh t`fnf frrhr cntf fntrcoc scdth un`tcr`h. k) Fd s`stfgc fn dczh bfrrco bfrrcoh h fs `nfstckdf. b) Fd s`stfgc fn dczh ck`frth t`f t`fnf nf gãs bfrhs quf phdhs. o) Fd s`stfgc t`fnf bfrhs fn fd hrì hrìfn. fn. B2 (3.; p) Rfc un s`stfgc bhn rfcd`gfntcb`òn un`tcr`c nfict`vc bdãs`bh. O`kuecr fd duicr of dcs rcçbfs fn dhs sìu`fntfs bcshs y bhgfntcr dhs rfsudtcohs shkrf fstck`dòco (s`fgprf fstckdf, `nfstckdf, c trcghs) o`b`fnoh s` hburrf pcrc icncnb`c pfqufóc, `ntfrgfo`c h ircnof.   

3    33  3=

c

  

3    33  3=

k

Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

  

b

3   3

  

3

   ;  3

o

Fnunb`cohs Fnunb` cohs ]rãbt`bcs ]rãbt`b cs Cudc

66

Junocgfnths of Cut Cuthgãt`b hgãt`bc. c.

Fnunb`cohs ]rãbt`bcs Cud Cudc c

][HKDFGC (2.?p) Fn fd fqu`ph of dc Jìurc 3 sf prhbfsc un b`frth prhoubth quf ddfic c unc J _ tfgpfrcturc _` (µB) y scdf c tfgpfrcturc _ (µB), dc bucd ofpfnof ofd bcuocd J _` (g 2/a) of prhoubth. C su vfz fd bcuocd bcuocd J pufof gho`j`bcrsf gfo`cntf unc vãdvudc of rfiudcb`òn Jìurc 3 bhgcnococ phr unc sfócd u (%). Rf ac rfcd`zcoh un pcr of fxpfr`gfnths fn dhs bucdfs, pcrt`fnoh of unc s`tucb`òn fstcb`hncr`c fn dc quf _` 7 6µB, _ 7 3=µB y u 7 ;= % sf ac `nbrfgfntcoh krusbcgfntf dc sfócd c dc vãdvudc acstc ;; % hktfn`ànohsf unc fvhdub`òn of dc tfgpfrcturc _ fn µB bhgh sf gufstrc fn dc Jìurc ;.

Jìurc ; Ofd g`sgh ghoh, pcrt`fnoh ofd g`sgh punth, s` sf gcnt`fnf bhnstcntf J , y _ ` `   oc un scdth acstc 1µB, sf hkt`fnfn dhs vcdhrfs of _ quf sf gufstrcn fn dc jìurc 2.

Jìurc 2 Rf pòf5 c) Bcdbudcr un ghofdh quf rfdcb`hnf rfdcb`hnf dcs pr`nb`pcdfs pr`nb`pcdfs vcr`ckdfs ofd s`stfgc y o`kuecr fd bhrrfsphno`fntf bhrrfsphno`fntf o`circgc of kdhqufs.(3p) kdhqufs.(3p)   k) ¸]horçc fstf s`stfgc s`stfgc prfsfntcr fd jfnògfnh jfnògfnh of rfshncnb`c rfshncnb`c rfspfbth c bcgk`hs bcgk`hs fn dc tfgp tfgpfrcturc frcturc of fntrcoc8 Of sfr csç, buãd sfrçc fd vcdhr of dc jrfbufnb`c of rfshncnb`c rfshncnb`c y fd p`bh of rfshncnb`c8 (=.2p) (=.2p)   b) ]rhphnfr un fsqufgc of rfiudcb`òn of dc tfgpfrcturc _ y o`kuecr fd bhrrfsphno`fntf o`circgc of kdhqufs `no`bcnoh dcs vcr`ckdfs gcn`pudcocs, bhntrhdcocs, rfjfrfnb`c y phs`kdfs pfrturkcb`hnf pfrturkcb`hnfs. s.(=.2p) (=.2p)   o) R`nthn`zcr fd rfiudcohr rfiudcohr of tfgpfrcturc tfgpfrcturc bhn fd br`tfr`h of hktfnfr unc unc rfspufstc s`n frrhr fstcb`hncr`h cntf cntf fntrcocs fsbcdòn fn dc rfjfrfnb`c. (3.2p) (3.2p)   f) R` dc tfgpfrcturc of fntrcoc fntrcoc `nbrfgfntcrc d`nfcdgfntf su vcdhr c rczòn of =.3µB/sfb. =.3µB/sfb . ¸Buãd sfrçc fd vcdhr ofd frrhr bucnoh sf cdbcnbf unc s`tucb`òn fstcb`hncr`c8 (=.6p) (=.6p)   Junocgfnths of Cut hgãt`bc. hgãt`b c. ;=36 ;=36-3: -3:

Enunciados Problemas 1516 Pepcan v01

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