ISM - Introduction - To - Power - Elecronics - Hart
August 10, 2022 | Author: Anonymous | Category: N/A
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GEKY^MS ; W@B]^L@JW
(;-;)
(;-3)
3=T
39T
;=T
;9T
=T
9T
-=T 9s
3us
>us
4us
5us
;9us
;3us
;>us
;4us
;9us
;3us
;>us
;4us
T(N;13)
^lom
3=T
(;.>777u,37.599) 39T
;=T
;9T
=T (>.9577u,-5=;.4us
4us
5us
T(W;1>)
^lom
Lj pkrt (c), tem v`btkfm kgr`ss tem gurrmjt s`urgm ls rmnugmn dr`o 3> T cy tem swltge rmslstkjgm kjn nl`nm v`btkfm nr`p.
(;-7)
>9 T
4j,37.) 39 T
(7.;=9u,-;.9=3)
9T
(7.;=9u,-;.9=3)
-39T 9s
=us
; 9 us
T(T31-)
^lom
; =u s
(;->)
3=T
(599.999j,37.) 39T
;=T
;9T
=T (7.5777u,-;.9=;6) 9T
-=T 9s
3us
>us
4us
5us
T(T31-)
^lom
;9us
;3us
;>us
;4us
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
GEKY^MS 3 W@B]^L@JW 3/3;/;9
3-;) Wqukrm wkvms kjn trlkjfubkr wkvms d`r v`btkfm kjn gurrmjt krm tw` mxkopbms. PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-3)
k) p ( t )
? v( t) l( t) ?
v 3 ( t ) S
?
X;6 ;69slj 9slj ( 766t ) _3
? 35slj3ωt K.8 p(t) ? v(t)l(t) ? 39 slj33ωt V.8 Y ? ;9 V. c) 7slj>ωt K.8 p(t) ? ;=slj(3ωt)s ;=slj(3ωt)slj(>ωt) lj(>ωt) V.8 Y ? 9 PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3->)
k) 9 2 t 2 =9 os
9 p ( t ) ? v ( t ) l ( t ) ? >9 9
=9 = 9 os 2 t
2 69 os 69 o s 2 t 2 ; 99 o s
c) Y ?
; ^
^
;
69 os
∨ v ( t ) l ( t ) nt ? ;99 os ∨ >9 nt ? 5.9 V . 9
=9 os
g) 69 os
^
V
? ∨ p ( t ) nt ? 9
∨ >9 nt ? 599 oA .8
`r V
? Y^ ? ( 5V ) ( ;99 os ) ? 599 oA .
=9 os
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-=)
k)
69 V . ∓= 9 V . p ( t ) ? v ( t ) l ( t ) ? >9 V . 9
9 2 t 2 4 os 4 os 2 t 2 ;9 os ;9 os 2 t 2 ;> os ;> os 2 t 2 39 os
c) ;9 os ;> os 4 os 6 9 = 9 > 9 Y ? ∨ p ( t ) nt ? nt nt nt + ∓ + ∨4os ( ) ;9∨os ? ;< V . 39 os ∨9 ^ 9
;
g)
^
;
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
;9 os ;> os 4 os V ? ∨ p ( t ) nt ? ∨ 69 nt + ∨ ( ∓=9 ) nt + ∨ >9 n t ? 9.75 A .8 9 4 os ;9 os 9 `r V ? Y^ ? ( ;< ) ( 39 os ) ? 759 oA . ^
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-4) Y ? Tng L kvf kvf k) L kvf ? 3 K., Y ? ( ;3 ) ( 3) c) L kvf ? 7.; K.,
3> V . ? 3> Y ? ( ;3 ) ( 7.;) ? 76.3 V .
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-6) k)
? l ( t ) S ? 3= ssllj 7 66 66t T . slj 76 7 66t ) ( ;.9 ssllj 7 66 66t ) ? 3= sl slj 3 766t ? ;3.= ( ; ∓ g` g`s 6= 6=>t ) V . p ( t ) ? v ( t ) l ( t ) ? ( 3= sl v S ( t )
^
Y S
; p ( t ) nt ? ;3.= V . ? ^ ∨ 9
c) v B ( t ) p B ( t )
nl ( t )
?B
nt
? ;9 ( ;9 ) ∓7 ( 766 ) ( ;.9 ) g`s 77666t ? 7.66 g` g`s 7 76 66t T . 7.66 66) ( ;. ;.9 9) ( 7.
? v ( t ) l ( t ) ? ( 7.66 g` g`s 76 766t ) ( ;.9 sl slj 7 76 66t ) ? Y B
g)
p ( t )
?
;
3
slj 6 6= =>t
? ;.5< ssllj 6= 6=>t V .
^
∨ p ( t ) nt ? 9
^ 9
766t ) ? ;3 ssllj 76 766t V . ? v ( t ) l ( t ) ? ( ;3 ) ( ;.9 ssllj 76 Yng
?
;
^
∨ p ( t ) nt ? 9
^ 9
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-5)
Smslst`r1
? l ( t ) S ? 5 + 3> slj 3ω 4499t T . p ( t ) ? v ( t ) l ( t ) ? ( 5 + 3> sl slj 3ω 4 49 9t ) ( 3 + 4 sl slj 3ω 49 49t ) slj 3ω 49 49t + ;>> sl slj 3 3ω 49 49t V . ? ;4 + slj 3 3ω 49t
Ljnugt`r1 Y B ? 9. ng s`urgm1 Yng ? L kvfTng ? ( 3 ) ( 4 ) ? ;3 V . PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3- ) ( ; 9 ) ∓7 ? 7 .4
K.
k) V
?
; 3
Bl
3
;
3 ? ( 9.;) ( 7. 7.4 ) ? 9.4>5 A .
3
c) Kbb st`rmn mjmrfy ls kcs`rc kcs`rcmn mn cy S1 VS ? 9.4>5 A. g) Y S
?
V S ^ YW
?
9.4>5 >9 os
? ;4.3 V .
? YS ? ;4.3 V .
n) J` gekjf gekjfmm lj p`wmr ssuppblmn uppblmn cy ttem em s`u s`urgm1 rgm1 ;4.3 V. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-;;) k) V
?
l( t)
; 3
?
3V
B l 3 , `r l ? ;
t
B
∨
B
v( θ ) nθ
?
3 ( ;.3 )
?
;
9. 9;9
? ; = .> <
K.
t
;> n θ ? ;>99t K.
∨
9.9;9 9 ;=.> ;=.>< < ? ;>99 ;>99t `j
9
? ;;.; os
t`j
c) Mjmrfy st`rmn lljj B oust cm trkj trkjsdmrrmn sdmrrmn t` tem rmslst` rmslst`rr lj (39 - ;;.;) ? 5.< os. os. Kbb`wljf dlvm tlom g`jstkjts, ώ ≮
B S
?
5.< os =
? ;.6 os.8
S≭
B ;.6 os
?
;9 oE ;.6 os
? =.43 ℤ
PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-;3) k) l(t) ? ;599t d`r 9 2 t 2 > os l(> os) ? 6.3 K.8 VBpmkh ? ? ;.39os
49os
5 9o s
;99os
-V(Tgg) ^lom
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-;7) k) ^em zmjmr nl`nm crmkhs n`wj wemj tem trkjsls trkjslst`r t`r turjs `dd t` okljtklj ljnugt`r gurrmjt. gurrmjt. c) Wwltge gb`smn1 9 2 t 2 39 os. v B nl
? ;3 T . ? B
nl B ( t ) nt
;3
v
nt ? B ? 9.96= ? ;49 K/s kt t ? 39 os, l B ? ( ;49 ) ( 9.93 ) ? 7.3 K. B
B
Wwltge `pmj, zmjmr `j1
? ;3 ∓ 39 ? ∓5 T . ∓5 v ? B? ? ∓;94.6 K/s v B
nl B nt
∄t ?
B 9.96= ∄t t` rmturj t` zmr` 1
∄l ∓;94.6
?
∓7.3 79 ? os ∓;94.6
^emrmd`rm, ljnugt`r gurrmjt rmturjs t` zmr` kt 39 + 79 ? =9 os. lB ? 9 d`r =9 os 2 t 2 69 os. g) >9oV
Ljnugt`r ljst. p`wmr 9V
->9oV
V(B;)
59oV
Qmjmr ljst. p`wmr >9oV
WMB:: 9V 9s
;9os V(N;)
39os
79os
> 9o s ^lom
= 9o s
49os
69os
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
n)
? 9.
Y B
?
Y Q
;
^
∨
^ 9
pQ ( t ) nt
?
; 9.97 4> ? ;7.67 V . 4 > ( ) ( ) 9.96 3 ;
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-;>) k) ^em zzmjmr mjmr nnl`nm l`nm ccrmkhs rmkhs nn`wj `wj w wemj emj te temm trkj trkjslst slst`r `r tu turjs rjs `dd `dd t` okljtk okljtklj lj ljn ljnugt` ugt`rr gurr gurrmjt. mjt. c) Wwltge gb`smn1 9 2 t 2 ;= os. v B nl B
? 39 T . ? B
nl B( t ) nt
39
? vB ?
? >99 K/s nt B 9.9=9 kt t ? ;= os, l B ? ( >99 ) ( 9.9;= ) ? 4.9 K.
Wwltge `pmj, zmjmr `j1 79 ? ∓;9 T . ? 39 ∓ 79 ∓;9 v ? B? ? ∓399 K/s
v B nl B nt
B 9.9=9 ∄t t` rmturj t` zmr` 1
∄t ?
∄l ∓399
?
∓4.9 ? 79 os ∓399
^emrmd`rm, ljnugt`r gurrmjt rmturjs t` zmr` kt ;= + 79 ? >= os. lB ? 9 d`r >= os 2 t 2 6= os. g) 399V
Ljnugt`r ljst. p`wmr 9V
-399V V(B;) 399V Qmjmr ljst. p`wmr ;99V
WMB:: 9V 9s
39 os
> 9o s
V(N;)
^lom
49 os
5 9o s
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
n) Y B Y Q
? 9. ;
?
^
∨
^ 9
pQ ( t ) nt
?
; ( 9.97 ) ( ;59 ) ? 74 V . 9.96 9.96= = 3 ;
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-;=) Mxkopbms krm squkrm wkvm (Tros (Tros ? To) kjn k trlkjfubkr wkvm (Tro (Tross ? To/∑7). PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3 3 9 .= ) 3-;4) Yeksm g`jnugt`rs1 Yτ ? L S ? ;3 ( 9.
? 63 V . 3
Jmutrkb g`jnugt`r1 Y J ? L 3 S ? ( ;3 7 ) ( 9.= ) Yt`tkb S J
? 3;4 V .
? 7 ( 63 ) + 3;4 ? >73 V .
?
Y J L J 3
?
63
( ;3 7 )
3
? 9.;46 ℤ
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-;6) Sm1 Yr` Yr`c. c. 33-> ->
? To L ros ? L o Tros
9.6 ? 5.76 T . ? ;9 9. 9.= ? 3.57 K. N ? > 9. N
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-;5) Sm1 Yr` Yr`c. c. 33-= -= Tros L ros
? To ?
N
;> ? ;9 ö ? 5.74 T . 39
;
9.994
9.93
9
9.9;
9.93
3
6 nt +
( ∓=) nt +
3
>3 nt
?
36.6
? =.34
K.
∨ PPPPPPPPPPPPPPPPPPPPPPPPP ∨ ∨ PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 9.994
9.9;
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-;.=5 T . ö ö 3 3 K.
3
= 3 7 ;.; ? ( 3.9 ) ( ;.=) + ö ö g`s ( ∓39¹) + ö ö 3 3 3 3 49t ∓ ;7=¹ ) J`tmtekt J`tm tekt ∓ g`s(>ω 49t + >=¹) ls g`s ( >ω 49
g`s ( ∓;;=¹ )
? 6.9 V .
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-39) ng 1 T9
? 7 ( ;9 9 ) ? 799 T .
ό;
? 3ω 49 1 L T ; ? ; ?
\;
? >ω 49 1
\3
\;
? ;/ S + aό G ? 9.9; + a 9.9;5< > ∩9 ? ; 5 6 ∩ ∓ 4 3 .; ¹ 9.9; + a 9.9;5 9;5< ) ( 9.9
? ;/S + aό G ? 9.9; + a 9.9766 4∩ 9 L ? ;=7∩ ∓ 6=.;¹ T 3 ? 3 ? 766 ) \3 ( 9.9; + a 9.9766
ό3
Y ? T9 L 9 +
√
∛ T 3L
o o
g`s ( ε j ∓ τ j )
j ?;
( ;56 ) ( > )
? 79 9 ( = ) +
g ` s ( 4 3 .; ¹ )
( ;= 7 ) ( 4 )
+
3 ? ;=99 + ;6= + ;;5 ? ;6 V . >
Smslst`r1
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3 Y ? L ros S
L ros
?
L 93 + L;,;3,ros L 9
L;
?
L 3
?
+ L 33,ros
? + a ( >ω 49 ) ( 9. 9.9;) ;9 > + a ( 5ω 49 ) ( 9. 9.9;)
? 7.=; K. ? 9.4> 9.4>; ; K.
3
3
7.=; + 9.4>; ? ) Y ? T9 L 9 +
√
∛ T 3L
o o
g`s ( ε j ∓ τ j )
j ?;
j 9 ;
Tj =9.9999 =9.9999
εj - ϝj¹ 9 34.4
Lj ;9.9 ;9.9
Yj =99.9 337.4
37 3;=4..94949496 3;..=;; >==4..97 3=3.;.; > ;3.=999 9.43= 47.> ;.6 ^er`ufe j ? >, ∛Yj ? 6=7 V. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-3=) Y ? T9 L 9 +
√
∛ T 3L
o o
g`s ( ε j ∓ τ j )
j ?;
L 9
?
Y9, S
T9 ∓ T ng S
∓ ? =9 74 ? 9.6 39
K
? L 93 S ? ( 9.6 ) 3 39 ? ;.6; ;.99 33.>> =;.;4 9.57 ;.;6 4.56 > 7;.57 4=. 9.>5 ;.34 3.77 = 3=.>4 5;.9= 9.7; ;.73 9. TK. W ? Tro ross L ro ross ? ö 3 Y 674 pd ? ? ? 9.6;< W
;93>
g) ND ?
L ;,ros L ros
?
;9/ 3 5.=;
? 9.57;
n)
^EN L ?
4
3
+ 7 ö ö 3 3
3
? 9 .4 6 ? 4 6 %
;9 ;9// 3
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-35) k) Y ?
∛ Y ? ;639ö ;33ö j
g`s ( >9¹ )
+ 9 + 9 ? 65; V .
c) 3
3
3
;3 = > ?
4.73
4.73
3
;7=5
3.53
=.44
?
>
?
? 9.5< 9.5>4 4 ? >>.4 >>.4% %
? 5
4.73
L ros
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP 3-79) L;,ros L ros
?
?
;3 3
? 5 .> <
5.>9 ) ( ;9.4 ) g`s ( 9 ) ? 3974 V .
3974
?
ros ros Tros L ros
K.8
? 9.59 9.59 ? 59 59% %
3>9 ) ( ;9.4 ;9.4) ( 3>9
? 4.74 ? 9.49 ? 49% ;9.4
? 5.>< ? 59% ;9.4
grmstt dkgt`r ? m) grms
L pmkh L ros
?
;5.7 ;9.4
? ;.63
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-7;) =T1
L ? 9 (gkpkglt`r ls kj `pmj glrgult)
3= g`s(;999t ) 1 Q
?
S + aό B ∓ a
;
ό G
? 3+
a;999(.99; ) ∓ a
; ;999( ;999) ;9 ∓4
?3+
a9
3= L
?
g`s(;999 g`s( ;999 ) ;3.=g`s(;999 ;3.=g`s(;999 ) t ? t K 3
;9 g` g`s( 3999t ) 1 Q L;9
?
;9 3 + a;.=
?3+
a;.= ℤ
? >∩ ∓ 76¹ K. 3
3
;3.= > L ros ? ö + 3 ö ? 99V V (L ; )
K TF ( V ( L ; ) )
L (L ; )
>os T (T ; 1 + )
39 9 WMB:: -3 9 9s
5os
;3os
; 4o s
39os
^lom
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-77) Kvmrkfm Kvmrkfm p`wmr d`r tem rrmslst`r mslst`r ls kppr`xloktmby ;999 V. D`r tem ljnugt`r kjn ng s`urgm, s`ur gm, tem kvmrkfm p`wmr ls zmr` (sblfetby nlddmrmjt cmgkusm `d juomrlgkb s`butl`j).
3.9HV Kvmrkfm Y`wmr
(;4.469o,9.. 9 Ljnugt`r 3. 9 (>.9999o,4>5.996o)
Smslst`r (>9.93;o,4>6.4
9 9s L (B ; )
;9os W (V ( B ; ) )
39os W(V(S;))
79os
>9os
^lom
^em ljnugt`r pmkh mjmrfy ls 4>< oA, oktgeljf tem rmslst`r kcs`rcmn mjmrfy. ^em s`urgm p`wmr ls -;4.3 V kcs`rcmn, omkjljf ;4.3 V suppblmn. c) Ld tem nl`nm kjn swltge pkrkomtmrs krm gekjfmn, tem ljnugt`r pmkh mjmrfy ls 47= oA, kjn tem rmslst`r kcs`rcmn mjmrfy ls 439 oA. ^em nlddmrmjgm ls kcs`rcmn cy tem swltge kjn nl`nm. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-74)
^em ljnugt`r gurrmjt rmkgems k okxlouo vkbum `d 7.> K wlte tem rmslstkjgms lj tem glrgult1 L ? 6=/ (39+;+;) ? 7.> K. >.9K
Ljnugt`r Gurrmjt
3.9K
WMB:: 9K L(B;) >.9K W`urgm Gurrmjt 9K
->.9K 9s
39os
>9os
49os
5 9o s
-L(T;)
^lom
[ukjtlty
Yr`cm Mxprmssl`j
Smsubt
Ljnugt`r rmslst`r kvmrkfm p`wmr Wwltge kvmrkfm p`wmr Nl`nm kvmrkfm p`wmr W`urgm kvmrkfm p`wmr
KTF(V(S;))
66.; V
KTF(V(W;)) KTF(V(N;)) KTF(V(Tgg))
7.54 V mkge 5; oV mkge -5=.9 V
;99os
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
3-76) k) Y`wmr kcs`rcmn cy tem lljnugt`r jnugt`r ls zmr`. Y`wmr kcs`rcmn cy ttem em Qmjmr nl`nm ls ;7.5 V V..
>.9K
3.9K Ljnugt`r Gurrmjt
9K L(B;) >.9K
3.9K
WMB:: 9K 9s
Qmjmr Nl`nm Gurrmjt
;9os -L(N;)
39os
79os
> 9o s
= 9o s
49os
69os
^lom
c) Y`wmr lj tem ljnugt`r ls zmr`, cut p`wmr lj tem ;.=ℤ rmslst`r ls ;.64 V. Y`wmr kcs`rcmn cy tem Qmjmr nl`nm ls 4.7= V. Y`wmr kcs`rcmn cy tem swltge ls 777 oV. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
7-75) Wmm Yr`cbmo 7-76 d`r tem glrgult nlkfrko. k) Y`wmr kcs`rcmn cy tem Qmjmr nl`nm ls 74.; V. Y`wmr kcs`rcmn cy tem ljnugt`r ls zmr`. ;9 K
=K
Ljnugt`r Gurrmjt
WMB:: 9K L(B;) ;9 K
=K
Qmjmr Nl`nm Gurrmjt
9K 9s
3 9o s
>9os
49os
59os
-L(N;)
^lom
c) Y`wmr lj tem ljnugt`r ls zmr`, cut p`wmr lj tem ;.=ℤ rmslst`r ls >.> V. Y`wmr kcs`rcmn cy tem Qmjmr nl`nm ls ;>.3 V. Y`wmr kcs`rcmn cy tem swltge ls 65> oV.
Dubb dlbm kt ettp1//tmstckjh749.mu/s`butl`j-okjukb-p`wmr-mbmgtr`jlgs-;st-mnltl`j-ekrt
3-79 K
^`tkb Gurrmjt
39 K
9K
-39K 9s L (L ; )
>os L (L 3 )
L (L 7 )
5os L (L > )
;3os - L( T ; ) ^lom
; 4o s
[ukjtlty
Yr`cm Mxprmssl`j
Smsubt
Y`wmr ros gurrmjt Kppkrmjt p`wmr W Y`wmr dkgt`r
KTF(V(T;)) SOW(L(T;)) SOW(T(L;1+))* SOW(L(T;)) KTF(V(T;)) / (SOW(T(L;1+))* SOW(L(T;)))
4=9 V ;> K 4> V. Kvmrkfm Kv mrkfm Ljnugt`r Y`wmr Kvmrkfm Ljnugt`r T`btkfm Kvmrkfm Smslst`r Y`wmr Mjmrfy Kcs`rcmn cy Smslst`r Mjmrfy Kcs`rcmn cy Nl`nm Mjmrfy Kcs`rcmn cy Ljnugt`r
okx ? >.= K. okx ? 3.93= A 9.9;9 V. -39.7 V. 9.>4> V.
>.7< K ;.< V
. 9 . 9
;= A 9
ros Smslst`r Gurrmjt
9.5 >5 59 9 V.
;69
n ) W ? ro ? T ? ros s Lro ros s ?
mm) pd pd ?
?
W W
3
V >59 V
Y Y
T (= (= =...4 4 44 4 4)) ? 4 46 6 6< < TK K.
TK 46< TK
?
9 9 9...6 6 69 96 6 ? 6 69 9 9...6 6% 6%
7-3) k ) L 9 T` `
?
;3 3 K K .88 L 9 ; .
?
?
T9
S
T9
?
;3 3 3)))( (3 39 9 9)) LL 9 S? (; (3
To ?T ? 3 p 3> > >9 9 6= = => > T . 8 T o `p p p ? 6 o p
T Tros J; J3
6=> ?
?
3 3>9 ?
=77
c ) L ` ? L ` ? L
?
= =7 7 77 7 T T. 9.>=
J3 J;
;3 ? ?
9.>=
?
3 34 4 4...6 6 K K.
3 3> > >9 9T .
?
7-7)
Tsros T To T T Y Y Y Y s, ros 8 LL ro 8T 8 T k) pd p d ? ? o r o os ss ? S S ,r ro o os ss ? ss , r ro o os ss ? 3 W Ts, rros S S 3 os os L L rros os os
To / S 3 / S T S 3 ; pd ? ? ? ? To T To 3 T Ts , rros T 3 os os L Lros ros 3 / S 3 3 Sros S, ros
ls pbkgmo g` `sss((q g` `ss( s(9 (9 9)) ? ; c c) Nlspbk N gmomjt mjtpd pd ? g` q; - d d) ? g` L L;; ?
T;
?
; To
S S S S 3
9 988 pd pd ? g` g` `ss( s(q 8 q;; - d d; ) ND ND
R
? ND ND
; 3
7->) ]sljfMq. 7->) ]sljf ]sljfMq.7-;=, 7-;=, wt T ssllj T k) l(w t) ? o o ((sssllj ? -q ) + T lj( j(w t - T lj q ) m -wwt/wt Q Q Q Q Q Q ? S S3 + (w B ) 3 B
S
?; ;3 3 3...5 5 V
766(9.9;3) ?9 9...7 7 74 4 4; ; rkn ;3 wB 766(9.9;3) wt ? ? ? ? ? 9.766 S ;3 t ) ? ; ;7 7...3 3 ssllj lj( j(w t - 9 9...7 74 4 4; ;) + > >...4 4 46 6 m -wt/9.766 7...= = =9 9 rk 39 9 9; l (w 7 7 1 c r k kn n ?3 ; w c ? 7
? tk tkj kj -; q ?
wB
3 6 ; ;3 3 + (7 (7 76 6 66 6((9 (9. 9..9 9 9; ; ;3 3) 3)) )) 3
?
? ? tk tkj kj
-;
c) L Lkvf ? > K. ( juomrlgkb ljtmfrktl`j) >...7 7 74 4 K g) LL r rooos ss
?4 ju uo ommmr rl r lg lgk gkb kb 4...6 69 9 K K. ( j uo 6
3 4 3 lj lj jt tm t mmf fr f rk k kt t tll` l` `j j) Y Y ss S S? ((4 ? LLr ro 4...6 6 69 9 9)) 3 ( ; ;3 3)) ? = =7 7 75 5V . o os
=75 ? Y ? ? ?9 n n) pd pd ? 9...4 4 46 6 W (;39)(4.69)
7-=)]sljfMq.7-;=,
T T T T wt o ssllj lj( j(w t - o ((sssllj lj q ) m -wwt/wt k) l(w t) ? ? -q ) + Q Q Q Q B Q Q ? S S3 + (w B ) 3
766(9.9;=) S ;9 wB 766(9.9;=) ? ? ? ? 9.=4= wt ? ;9 S
tkj kj -; ? tk q ?
wB
3 6 ; ;9 9 + (7 (7 76 6 66 6((9 (9. 9..9 9 9; ; ;= =) =)) )) 3
?
tkj kj ? ? tk
-;
?; ;; ; ;...= = V
9...= = =; ; ;= = ?9
rkn
t ) ? ; ;> >...5 5 ssllj lj( j(w t - 9 9...= =; ; ;= =) =) + 6 6...3 3 36 6 m -wt/9.=4= 7...4 4 4= = =6 6 rk 39 9 9< = 1 c r k kn n ?3 < w c ? 7 c) LL kvf ? = K. ( j ju uo om mmr rl r lg lgk gkb kb l lj lj jt t tmmmf fr f rk k kt t tll` l` `j j) =...9 9 9= = K u o g) LL r rooos ss
?6 ju uom ommr rl r lg lgk gkb kb 6...4 4= = K K. ( j uo 4
n n) pd p d ?
Y W
?
=5>
(;39)(6.4=)
?
3 6 9 lj lj jt t tmmmf fr f rk k kt tl t l` l` `j j) Y Y LLr ro ss S S ? ((6 ? 6...4 4 4= = =)) 3 ( ; ;9 9)) ? = =5 5 5> >V . o os
7 9 9...4 4 47 76 6 ? 4 47 7 7...6 6% 6%
7-4)]sljfMq.7-;=,
T T T T wt ? -q ) + k) l(w t) ? o ssllj lj( j(w t - o ((sssllj lj q ) m -wwt/wt Q Q Q Q Q Q ? S S3 + (w B ) 3 B
766(9.95) ;= wB 766(9.95) ? ? ? ? 3.9; wt ? S ;=
? tk q ? tkj kj -;
wB
6( ; ;= = 3 + (7 (7 76 6 66 6((9 9. 9..9 9 95 5 5))) )) 3
? ?
S
? ? tk tkj kj
-;
?7 77 7 7...6 6 V
?; ;...; ; ;; ;
rkn
lj w c ? > l (w 9 ; 1 c r k kn n ?3 9 t ) ? ; ;9 9...; ; ;sssl lj( j(w t - ; ;...; ;; ;) + < ...7 7 7= = rk 3= = =9
K. ( juomrlgkb ju juom gkb b ljtmfrktl`j) 56 6 K omrl rlgk c c)) L Lkvf ? > >..5 g) LL r rooos ss
?4 4...5 5> > 5
n n) pd p d ?
Y W
?
3 4 = K ju uo om ommr rl r lg lgk gkb kb lj lj jt tm t mmf fr f rk k kt t tll` l` `j j) Y Y LLr ro ss S S ? ((4 K. ( j u ? 4...5 5 5> > >)) 3 ( ; ;= =)) ? 6 69 9 9; ;V . o os
69;
(3>9)(4.5>)
?
3 9 9...> > >3 36 6 ? > >3 3 3...6 6% 6%
7-6)]sljfkjl!k"l`!#`!",$>5&'`kjk!kf!g*!jt`'3+.
5.9K
Gurrmjt Lkvf?3KdrS?>5!os >.9K (;".#99o$3.99%9)
KvmrkfmGurrmjt
9K 9s
=os L ( S; )
;9 os KTF( L(B;)) ^ lo m
;=os
3 9os
7-5) ]sljfMqs.7-3 ]sljfMqs.7-33kj7 3kj7-37, -37,
T T - ng k) l(w t ) ? Qo slj(w t - q ) S
+
Km
/ wt -wt
T To wt - q) + ng mk/wt slj(k S Q
K?
B )3 S3 + (w
Q ?
wB
q ? tkj -; wt ?
wB S
k ? slj -;
S
?
3 6(.96=) ; 9 3 + (76
?
? tkj
-;
766(.96=) ;9
766(9.96=)
Tng To
?
;9 ;99
3>9 3
?
? 79.9 V
? ;.37
rkn
3.57
? 9.3 .5; K . (juomrlgkb ljtmfrktl`j) YS ? L r3o s S ? (> .
Y W
?
7; 7 7+ 37; (3>9)(>.5;)
? 9. 9.>6 >63 3?
>6 >6.3 .3% %
7-5
?
To
;39 3
766(9.;3) ;3
? >4.5 V
? ;.7;
rkn
? 7.66
? 9.356
rkn ? ;4.>
l (w t ) ? 7.47slj(w 8 c ? >.94 rkn t - ;.7 ;) >.9 + 6.44m -wt/7.66 Lkvf
? ;.;3>
K . ( juomrlgkb ljtmfrktl`j) Yng
?
? 37 7
? Tng LLk vf ? ( >5)(;.;3>) ? =>.9
?
3
?
3
?
V .
c) L ro s ; .69 K . (juomrlgkb ljtmfrktl`j) YS L ro s S (;.69) (;3) 7>.= V . Y => =>.9 .9+ 7> 7>.= .= ? 9. g) pd ? ? 9.>7 >7= =? >7 >7.= .=% % W (;39)(;.69)
7-;9) ]sljfMq.7]sljfMq.7-77, 77,
l (wt ) ?
To Tn g t ) + (g`s k - g`s w (k - w t) wB wB -;
Tng
>5 ? slj ;39 3 -;
? 9.356 rkn . k ? slj To t) ? >.45 t) -; .37w t K.8 c >.=9 g `s(w c ? >.>57 rkn ? 3 =6 l (w
L`
?
;
3p
c
k
3.99 K.8 Yng l(w t )n (w t t ) ?
?
5) ?
7-73) C6=G. C6=G. +"k6=!f +"k6=!f!!sfl! !!sfl!s7= s7=lj ljt!g` t!g`"tkf! "tkf!s`* s`*g!. g!.+j$`j +j$`j9.9;'` 9.9;'`t! t! sltgkjj9.99;'`t!l`!(l!k"#`!").
7-77) K`#Mq.77-77) K`#Mq.7-4;, 4;, wt/;>.;
-
slj(w k ) l (w t) ? = ..9 + 3.3>
r kn
c
3p k
c) L ros ?
., Y l (w Yng t)n (w tt) ? ;. -6.=5 g`s w t - ;.5 3 w t K., ;. ; .79< wt ?
t) + (g`s k - g `s w
; L`
?
c
? 3p k l(w t)n (w t ) ;..3> <
7-7;) +tEtC, 7->;) +tEtC, wt
ls(w t ) ? ; wB s
k
To slj(w t ) n (w t ) + 9 ? To wB s
lN3 (*t ) ? L B - ls ? L B -
To
B w
Mg `s k - g`s w tD
Mg`s k - g` g`s wt D
s
lN3 (k + u ) ?
-
u
LBw Bs
To ?
L 9? B
k + u)D Mg`s k - g`s(k
g`s k + g`s(k + u)
? -
LB(s
To
g`s ; g`s k - -
To w Bs
- k
7->3)+f``s`"*tl`jlst`*s!kg`jt`""! 7->3)+f``s`"*tl`j lst`*s!kg`jt`""!k"'-k!!gtl'l!ltkj k"'-k!!gtl'l!ltkjlj*gt`lj lj*gt`ljs!l!sltt! s!l!sltt! >5-s`*g!kj!sls >5- s`*g!kj!slstkjg!(Kl tkjg!(Klf.7-;=). f.7-;=).!sltgl"" !sltgl""gkjf!t!!"kkjf"! gkjf!t!!"kkjf"!`' `' t! 2:$t``*g!t!t`!q*l!`!"!!"s.!k"*!s`'t!!"kkjf"!!!j`j t! k"*! k"*! s!"!gt s!"!gt! ! '` t! lj*gt lj*gt` `. . ls ls s`"*tl s`"*tl`j `j k`ls k`ls kljf kljf !slst !slstkjg kjg!, !, t!! t!! k`lljfljt`*gljf`!"`ss!s. 7->7)2!!k"glg*ltgkjkgg`#"lstls`A!gtl!,ljg"*ljft!k"'-k!!gtl'l!`'Klf.7-3k kjk"'-k!!gtl'l!ltk'!!!!"ljfl`!`'Klf.7-6, kjk"'-k!!gtl'l! ltk'!!!!"ljfl`!`'Klf.7-6,!kglt!slstkjg!k!. !kglt!slstkjg!k!. +j`t!s`"*tl`jlst`*s!t!g`jt`""!k"'-k!!gtl'l!`'Klf.7-;>k*tltj` !slstkjg!.!kjk"sls`'tktglg*ltls"l!tkt`'Klf.7-4*tlt`*tg.! !s*"tljfk"*!`'Cls6=G,`tklj'`#k2lg!sl#*"ktl`j.kts`"*tl`jlsf`` !gk*s!j`!slstkjg!lsj!!!,kj"`ss!sk!j`tljt !gk*s!j`!slstkjg!lsj!!!,kj "`ss!sk!j`tljt`*g!. `*g!. 7->>kj7->=)!g`jt`""!k"'-k!!gtl'l!`'Klf.7-;=(lt`*tt!!slstkjg!)gkj! *s!t`sktls't!!slfjs!gl'lgkt *s!t`sktls' t!!slfjs!gl'lgktl`j.!k"*!`' l`j.!k"*!`'t!!"kkjf"!!!js t!!"kkjf"!!!js`jt!k"*! `jt!k"*! s!"!gt!'`t!lj*gt`.
GEKY^MS = W@B]^L@JW
7/59
?
T o 3
3
c)
Y ? T ` ,ros S
g)
pd ?
W
λ ω
λ ? 49¹
3
Y
;∓
?
n ) L kvf ,WGS
?
L ros,WGS
?
?
3ω S
3ω
⇓
? T ros
;∓
? >7; T 8
T` , ros
λ ω
+
slj( 3λ )
L ` , ros
3ω
?
? 7695 V
Y
?
7695 >59 9 ) ( 5. 5.4; 4;) ( >5
( ; + g`s λ ) ?
T ` ,ros S
?
5.4; 3
? 9.559 3 3ω ( =9 )
? 4.;
K
3
L ` ,ros 3
slj(3λ )
>7; =9
Tro ross L ro ross
T o
+
( ; + g`s 49¹) ? 7.3> K
?
>7; =9
? 5.4;
K
m) L;,ros
>59 ≅ 9.5> ö ? 5.9 K =9
^EN L
∓ L ;,3ros ?
L r3os
?
5.4;3
∓ 5.93
9.75 75 ? 75% 75% ? 9.
5.9
L ;,ros
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
=-3) k)
To
T`,ros
? ;39
T o
λ ? >=¹
T `3,ros
Y?
g)
pd ?
S Y W
n ) L kvf ,WGS
L ros,WGS
λ ω
;∓
3
3
c)
m) L;,ros
?
?
slj(3λ ) 3ω
⇓
T`, ros
? T ros
;∓
λ ω
? ;;>.> T 8
+
slj( 3λ ) 3ω
L `,ros
?
39 Y
Tros L ro ross
4== ;39 9 ) ( =. =.63 63) ( ;3
S
? 9.=¹ ) ? 3.79 K ? 3T 3ω ( 39 ) ω S ( +
?
L `,ros 3
?
=.63 3
? >.9=
K
;39 ≅ 9..>3
+
?
;;>.> 39
? =.63 K
;,ros ;,ros
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-7) Y ?
T `3.ros
⇓
S
;46.7
dr`o Dlf . =.3,
L `,ros
?
L WGS,ros
T `,ros
?
3>9
?
S
L `,ros 3
T`.ros
;46.7 7=
?
? ( 599 ) ( 7=) ? ;46.7 T
YS
? 9.6 ⇓
λ ≅ .65 K
>.65
599 pd ? Y ? W ;39 ( >.65 )
?
3
? 7.75 K
.69 ? 69% ? 9.69
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
=->) Vlte te t em 3> 3>9-T s` s`urgm, T` ,ros
;39
? ;39T 8
`r s`bvljf Mq. =-7, ;39 ∓ 3>9 ; ∓
λ ω
sl slj(3 j(3λ )
+
3ω
3>9 T s`urgm 1 T`,pmkh ? 3 ( 3>9 ) slj ( ;;>¹ ) ;39 T s`urgm 1 T`, pmkh
? To ?
3 ( ;39 )
? 9. = 8
3>9
Dlf.=.3 k ≅ ;;= dr`o Dl
? 9 ⇓ λ ? ;.¹
? 7;9 T
? ;69T
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-=) D`r Y ? 399 V , T` ,ros
?
YS
?
399 ( >9 )
? 5 T
]sljf Mq. =-7, 5 ∓ ;39 ; ∓ pd ?
Y W
?
λ ω
Y Tros ros L ros ros
+
slj( slj(3 3λ )
?
3ω
? 9 ⇓ λ ? ;.>5 rkn ? 5=¹
399 ;39 9 ) ( 59) ( ;3
9.6= 6= ? 6=%. 6=%. ? 9.
D`r Y ? >99 V , T` ,ros
?
YS
?
>99 ( >9 )
? ;34 T
Wljgm ;34 T : ;39 T `d tem s`urgm, >99 V ls j`t p`sslcbm. ^em okxlouo p`wmr kvklbkcbm ls
;39 3 >9
? 749 V.
^em pd ls ;.9 d`r 749 V.
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
=-4)
]sljf tem glrgult `d Dlf. =-;k, D`r Y ? 6=9 V , T`,ros
?
YS
?
6=9 ( 73 )
? ;=>.< T
]sljf Mq. =-7, ;=>.< ∓ 3>9 ; ∓
λ ω
+
slj( slj(3 3λ ) 3ω
D`r Y ? ; ;= =99 V , T` ,ros 3;< ∓ 3>9 ; ∓
λ ω
+
?
YS
slj( slj(3 3λ )
? 9 ⇓ λ ? ;.697 rkn ? K
3 ( 3>9 ) ( ; + g`s ( =4.=¹ ) ) ? 3.43 K 3ω ( 73 )
3(3>9 3(3 >9)) ? 7>9 7>9 T
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=-6) ]sljf tem glrgult `d Dlf. =-;k, D`r S ? 39ℤ, T`,ros
?
?
YS
;399 ( 39 )
? ;=>.< T
]sljf Mq. =-7, ;=>.< ∓ 3>9 ; ∓
λ ω
+
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+
slj( slj(3 3λ ) 3ω
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? 3;< T
9..< .< / 39 ? =.>5 K ? L ` ? ;=> 3
3
3>9 9) 3 ( 3> ( ; + g`s ( K 3ω ( 39 )
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=-5) S ?
T 3 Y
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Dr`o Dl Dlf.=-7, λ ≅ ;.¹
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+
slj ( 3λ ) 5ω
3ω
3 9 ≮λ
≮ ω
>ω
⇓
To
≮ T ` ,ros ≮
3
T o 3
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d`r λ; 2 όt 2 ω
kjn d`r ω
+ λ 3 2 όt 2 3ω
3ω ω 3 ( To slj όt ) n ( όt ) + ( To slj όt ) 3 n ( όt )ö T`.ros ? ö 3ω λ ω +λ
;
;
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∨
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+
slj ( 3λ; )
+ slj ( 3λ 3 ) >ω
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=-;;) k) ]sljf Mq. =-> K
3 n ) Y ? L ros S ? ( >.56 )
3
( ;5 ) ? >36 V
K
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?
>.;5
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3
( 33 ) ? 75> V
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όώ ? 9.6=>
? ;;.7 slslj ( ό t ∓ 9.4>4 ) ∓; =5 = 5m ∓ό t /9.6=>
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γ ? 7.45; rkn ? 3;;¹
K
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l ( όt )
λ
ε
? 9.=4; rkn 8
? ;;..;m∓ό t /9.435
;.333 rkn , ? 69¹ ? ;.
L ros
όώ ? 9.4.35 K
γ ? 7.4% dr`o tem YWplgm `utput dlbm usljf D`urlmr tmros ter`ufe j ? 99 V. (c) λ ≅ >4¹ d`r 699 V. WLJFBM-YEKWM T@B^KFM T@B^KFM G@J^S@BBMS (v`btg`jt.glr) *** @]^Y]^ T@B^KFM T@B^KFM LW T(7), @]^Y]^ G]SSMJ^ LW L(S) *** **************** LJY]^ YK YKSKOM^MSW SKOM^MSW ********************* .YKSKO .YK SKO TW ? ;39 8 s`urgm ros v`btkfm .YKSKO .YK SKO KBYEK ? 5; 8 nmbky kjfbm lj nmfrmms .W^MY YK YKSKO SKO KBYEK ;9 {S} B > 9 {B} **************** O@NMBW KJN G@OOKJNW ******************** .O@NMB NO@N N(j?9.9;) .O@NMB WO@N TWVL^GE (S@J?.9;) TG@J^S@B ;; 9 Y]BWM(-;9 ;9 {^KBYEK} {^KBYEK} 9 9 {YV} {;/D}) 8g`jtr`b d`r c`te swltgems .^SKJ .;OW =9OW 9OW ;u ]LG 8 `jm pmrl`n `d `utput .D@]S 49 L(S) 8 D`urlmr Kjkbysls t` fmt ^EN .YS@CM
.MJN
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-;4) O`nldy tem YWplgm glrgult dlbm `d Mxkopbm =-7. ]sm tem .W^MY YKSKO YKSKO g`ookjn (smm Yr`c. =-;=) d`r nmtmroljljf λ. (k) λ ≅ 59¹ d`r 499 V. (c) λ ≅ =6¹ d`r ;999 V. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-;6) ^em sljfbm-peksm v`btkf v`btkfmm g`jtr`bbmr `d Dlf. =->k ls sultkcbm d`r tels kppblgktl`j. Mqukt Mquktl`j l`j (=-¹. ^em (=-¹) ? ;47 T. =-;5) ^em YWplgm glrgult dlbm ls se`wj cmb`w. cmb`w. ^em t`tkb kvmrkfm b`kn p`wmr ls termm tloms tem p`wmr lj `jm `d tem peksm rmslst`rs. Mjtmr 7*KTF(V(SK)) 7*KTF(V(SK)) lj Yr`cm. ^em rmsubts krm (k) 4.>= hV d`r 39¹, (c) 3.6< hV d`r 59¹, kjn (g) >77 V d`r ;;=¹. J`tm tekt tem .W^MY YKSKO g`ookjn gkj cm usmn t` ruj tem termm sloubktl`js kt `jgm.
^ESMM-YEKWM T@B^KFM T@B^KFM G@J^S@BBMS -- S-B B@KN (7pevg.glr) *W@]SGM KJN B@KN KSM \\-G@JJMG^MN G@JJMG^MN (]JFS@]JNMN) ********************** LJY]^ YKSKOM^MSW **************************** .YKSKO .YK SKO Ts?>59 8 ros bljm-t`-bljm v`btkfm .YKSKO .YK SKO KBYEK?39 8 nmbky kjfbm lj nmfrmms .W^MY YKSKO KBYEK BLW^ 39 59 ;;=
.YKSKO S?7= .YKSKO 8 b`kn rmslstkjgm (y-g`jjmgtmn) .YKSKO .YK SKO B ? ;p 8 b`kn ljnugtkjgm .YKSKO .YK SKO D?49 8 s`urgm drmqumjgy ********************** G@OY]^MN YKSKOM^MSW ************************** .YKSKO .YK SKO To?{Ts*W[S^ To?{Ts*W[S^(3)/W[S^(7)} (3)/W[S^(7)} 8 g`jvmrt t` pmkh bljm-jmutrkb v`bts .YKSKO .YK SKO NBK\?{;/(4*D)} NBK\?{;/(4*D)} 8 swltgeljf ljtmrvkb ls ;/4 pmrl`n .YKSKO .YK SKO YV?{.=/D} ^K ^KBYEK?{KBYEK/(D*749)} BYEK?{KBYEK/(D*749)} .YKSKO .YK SKO ^SD?;9]W 8 rlsm kjn dkbb tlom d`r pubsm swltge g`jtr`b *********************** ^ESMM-YEKWM W@]SGM ************************** TKJ ; 9 WLJ(9 {TO} 49) TCJ 3 9 WLJ(9 {TO} 49 9 9 -;39) TGJ 7 9 WLJ(9 {TO} 49 9 9 -3>9) ***************************** WVL^GEMW ******************************** W; ; 5 ;5 9 WO@N 8 K-peksm N; 5 > NO@N W> > < ;< 9 WO@N N> < ; NO@N W7 3 ;9 39 9 WO@N N7 ;9 = NO@N W4 = ;; 3; 9 WO@N N4 ;; 3 NO@N
8 C-peksm
W= 7 ;3 33 9 WO@N
8 G-peksm
N= ;3 4 NO@N W3 4 ;7 37 9 WO@N N3 ;7 7 NO@N ***************************** B@KN ********************************** SK > >K {S} 8 vkj ? v(>,6) BK >K 6 {B} SC = =K {S} BC =K 6 {B}
8 vcj ? v(=,6)
SG 4 4K {S} 8 vgj ? v(4,6) BG 4K 6 {B} ************************* WVL^GE G@J^S@B ***************************** T; ;5 9 Y]BWM(-;9 ;9 {^K {^KBYEK} BYEK} {^SD} {^SD} {YV} {;/D}) T> ;< 9 Y]BWM(-;9 ;9 {^KBYEK+7*NBK\} {^KBYEK+7*NBK\} {^SD} {^SD} {YV} {;/D}) T7 39 9 Y]BWM(-;9 ;9 {^KBYEK+3*NBK\} {^KBYEK+3*NBK\} {^SD} {^SD} {YV} {;/D}) T4 3; 9 Y]BWM(-;9 ;9 {^KBYEK+=*NBK\} {^KBYEK+=*NBK\} {^SD} {^SD} {YV} {;/D}) T= 33 9 Y]BWM(-;9 ;9 {^KBYEK+>*NBK\} {^KBYEK+>*NBK\} {^SD} {^SD} {YV} {;/D}) T3 37 9 Y]BWM(-;9 Y]BWM(-;9 ;9 {^KBYEK+NBK {^KBYEK+NBK\} \} {^SD} {^SD} {{YV} YV} {;/D}) ************************ O@NMBW KJN G@OOKJNW ************************* .O@NMB WO@N NO@NTWVL^GE(S@J?9.9;) N .^SKJ .;OW =9OW ;4.46os ;9]W ]LG .D@]S 49 L(SK) 8 D`urlmr kjkbysls `d bljm gurrmjt .YS@CM .@Y^L@JW J@YKFM L^B=?9 .MJN
PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP
=-; ls usmn d`r tels sloubktl`j. Lj Yr`cm, mjtmr tem mxprmssl`j 7*KTF(V(SK)) t` fmt tem t`tkb termm-peksm kvmrkfm p`wmr lj tem b`kn, rmsubtljf lj 745 V. Wwltge W ; g`jnugts wemj tem gurrmjt lj peksm K ls p`sltlvm, kjn W> g`jnugts wemj tem gurrmjt ls jmfktlvm. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-39) ^em sokbbmst vkbum `d λ ls ;39¹. ^em g`jnugtl`j kjfmb oust cm bmss tekj d`r mqukb t` 49¹. ^em mxtljgtl`j kjfbm ls ;59¹, s` λ ls ;39¹ `r frmktmr. PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPP PPPPPPPPP =-3;) ^ESMM-YEKWM T@B^KFM G@J^S@BBMS -- S-B B@KN *O@NLDLMN D@S K NMB^K-G@JJMG^MN B@KN *W@]SGM LW \-G@JJMG^MN (]JFS@]JNMN) ********************** LJY]^ YKSKOM^MSW **************************** .YKSKO .YK SKO Ts?>59 8 ros bljm-t`-bljm v`btkfm .YKSKO .YK SKO KBYEK?>= 8 nmbky kjfbm lj nmfrmms .YKSKO .YK SKO S?3= 8 b`kn rmslstkjgm (y-g`jjmgtmn) .YKSKO .YK SKO B ? ;p 8 b`kn ljnugtkjgm .YKSKO .YK SKO D?49 8 s`urgm drmqumjgy ********************** G@OY]^MN YKSKOM^MSW ************************** .YKSKO .YK SKO To?{Ts*W[S^ To?{Ts*W[S^(3)/W[S^(7)} (3)/W[S^(7)} 8 g`jvmrt t` pmkh bljm-jmutrkb v`bts .YKSKO .YK SKO NBK\?{;/(4*D)} NBK\?{;/(4*D)} 8 swltgeljf ljtmrvkb ls ;/4 pmrl`n
.YKSKO YV?{.=/D} ^K .YKSKO ^KBYEK?{KBYEK/(D*749)} BYEK?{KBYEK/(D*749)} .YKSKO .YK SKO ^SD?;9]W 8 rlsm kjn dkbb tlom d`r pubsm swltge g`jtr`b *********************** ^ESMM-YEKWM W@]SGM ************************** TKJ 3; 9 WLJ(9 {TO} 49 49)9 9 -;39) TCJ TGJ 7 9 WLJ(9 {TO} 49 9 9 -3>9) ***************************** WVL^GEMW ******************************** W; ; 5 ;5 9 WO@N 8 K-peksm N; 5 > NO@N W> > < ;< 9 WO@N N> < ; NO@N W7 3 ;9 39 9 WO@N N7 ;9 = NO@N W4 = ;; 3; 9 WO@N N4 ;; 3 NO@N
8 C-peksm
W= 7 ;3 33 9 WO@N N= ;3 4 NO@N W3 4 ;7 37 9 WO@N
8 G-peksm
N3 ;7 7 NO@N ***************************** B@KN ********************************** SK > >K {S} 8 BK >K 3 {B} SC = =K {S} BC =K 7 {B}
8
SG 4 4K {S} BG 4K ; {B}
8
************************* WVL^GE G@J^S@B ***************************** T; ;5 99 Y]BWM(-;9 ;9 {^KBYEK+7*NBK\} {^K {^KBYEK} BYEK} {^SD} {^SD}{^SD} {YV}{YV} {;/D}){;/D}) T> ;< Y]BWM(-;9 ;9 {^KBYEK+7*NBK \} {^SD} T7 39 9 Y]BWM(-;9 ;9 {^KBYEK+3*NBK\} {^KBYEK+3*NBK\} {^SD} {^SD} {YV} {;/D}) T4 3; 9 Y]BWM(-;9 ;9 {^KBYEK+=*NBK\} {^KBYEK+=*NBK\} {^SD} {^SD} {YV} {;/D}) T= 33 9 Y]BWM(-;9 ;9 {^KBYEK+>*NBK\} {^KBYEK+>*NBK\} {^SD} {^SD} {YV} {;/D}) T3 37 9 Y]BWM(-;9 Y]BWM(-;9 ;9 {^KBYEK+NBK {^KBYEK+NBK\} \} {^SD} {^SD} {{YV} YV} {;/D}) ************************ O@NMBW KJN G@OOKJNW ************************* .O@NMB WO@N TWVL^GE(S@J?9.9;) .O@NMB NO@N N .^SKJ .;OW =9OW ;4.46os ;9]W ]LG .D@]S 49 L(SK) 8 D`urlmr kjkbysls `d bljm gurrmjt .YS@CM .@Y^L@JW J@YKFM L^B=?9 .MJN >9K
Lk 9K
WMB:: ->9K L(SK) =9K W`urgm
K
gurrmjt
9K
-=9K ;=os
39os -
3=os
79os
7=os
>9os
>=os
=9os
L(TKJ)
^lom
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W; (;.9999,=.=339K
W> L( S K)
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? 9.77
K.8 L S ,okx
Solj ?
(; ∓ .77 .77)(=.77 =.77)) 3(;99, 999)
39 3 ;3=
?
;3= 39
? 7.39 ℤ
? ;6.64 ½ E
4-;9) Bolj
?
(; ∓ N )( S) 3 d T`?= T
d
4.3= K.
? 399 hEz
Ts, T
N
L, K.
S, ℤ
Bolj, ½E
;9
9.=
9.=
;9
;3.=
;9
9.=
;.9
=
9.=
;9
4.3= ;4.6 (w`rst gksm, N ? ;/7, S ? ;9)
;.9
=
5.77
;= ;=
;/7 ;/7 B ?
(; ∓ Nolj ) Sokx
Bolj
3 d
; ∓ ; (;9) 7ö ? ? ;4.46 ½ E 3(3 3(399 h )
4-;;)
Mxkopbm nmslfj1 N ?
T ` T s
Bmt d
;= >5
? 9.7;3=
? ;99 hEz
Bmt ∄l B B ?
?
( d`r mxkopbm)
T ;= ? >9% `d L B ? 9.>9 ` ? 9 .>9 ö ? 9.6= K ö 5 S
( T s ∓ T` ) N ( >5 ∓ ;=) 9.7;3= ? ? ;76.= ½ E 9.6=) ;99,99 ;99,999 9 ( ∄l B ) d ( 9.6= ; ∓ N
G?
5 B
∄T `
? d
; ∓ 9.7;3= 5 ( ;=9 ) ;9∓4 (9.99=);99,99 ,999 9
? ;3.= ½ D
T ` ö
@temr vkbums `d B kjn G krm vkbln ld tem ljnugt`r gurrmjt ls g`jtlju`us wlte okrflj.
4-;3) (Cksmn `j tem mxkopbm nmslfj lj 4-;;)
Tokx, swltge ? Ts ? >5 T Tokx, nl`nm ? Ts ? >5 T Lokx, swltge ? LBokx ? ;.= + 9.6=/3 ? ;.56= K ;.56 56= = ) ? 9.=54K Lkvf, swltge ? T` L` ? ;= ( ;. Ts
>5
N^
;
l ( t) t) n t ? ;.94 K ( ju juomrlgkbby) ^ ∨
Lros, swltge ?
3 B
9
Lokx,nl`nm ? LBokx ? ;.56= K Lkvf,nl`nm ?LB- Lkvf,swltge ? ;.56= ‗ 9.=54 ? ;.35< K ;
^
l ( t) t) n t ? ;.=4 K (juomrlgkbby) ^ ∨
Lros,nl`nm ?
3 B
N^
4-;7) Mxkopbm nmslfj1 N ?
T ` T s
Bmt d
G
;= 3>
? 9.43=
? >99 hEz
Bmt ∄l B B ?
?
? >9% `d
( d`r mxkopbm) LB
? 9.>9 ( 3 ) ? 9.5 K
( T s ∓ T` ) N ( 3> ∓ ;= ) 9.43= ? ? ;6.4 ½ E 9.5 5 ) >99 >99,999 ,999 ( ∄l B ) d ( 9. ; ∓ N
? 5 B
∄T `
? d
; ∓ 9.43= 5 ( ;6.4) ;9 ∓4 (9. (9.9;)> )>9 99,99 ,999 9
T ` ö
4-;>) Mxkopbm nmslfj1 N ?
T ` T s
?
;3 ;5
? 9.446
? ;.46 ½ D
Bmt d
? 399 hEz
( d`r mxkopbm)
Y ` ;9V L B
? L ` ? T` ? ;3T ? 9.577 K
Bmt ∄l B
( T s ∓ T` ) N ( ;5 ∓ ;3 ) 9.446 ? ? 49 ½ E 9.777 7) 39 399,9 9,999 99 ( ∄l B ) d ( 9.77
B ?
G
? >9% `d L B ? 9.>9 ( 9.577) ? 9.777 K
?
; ∓ N
∄T 5 B `ö T `
? d
; ∓ 9.446 9.; 5 ( 49 ) ; ;9 9 ∓4 ö 399, 999 ;3
? 7.= ½ D
@temr vkbums `d B kjn G krm vkbln ld tem ljnugt`r gurrmjt ls g`jtlju`us wlte okrflj.
4-;=) j ?;
⇓
T ; ? 79.36
]sljf kg glrgult kjkbysls, T`; 9.95 T ? 3(9.9>5) ? 9.94> T . ∄T ` ;.>> ? ? 5%
k ) rG
;5
T `
∄
∄T `
c)
T `
T
≮ 9.=% T
∄ ` ≅∄
l r
` , MWS
=9(;9) ∓4 G
rG ?
?∄G G ⇓
∄T ` 9.99=(;5) 9.97; G l 3.55 G ⇓ ?∄ ? ? ℤ r
G
?
=9(;9) ∓4 r G
?
=9(;9) ∓4 9.97;
? ;499 ½ D .
4-;6) k ) T`
T s
?
39 ; ∓ .4
?
; ∓ N T s c) L B ? (; ∓ N ) 3 S L okx
?
L olj
?
g)
T s
(; ∓ N ) S
T s
(; ∓ N ) 3 S
∄T`
?
T` n ) L N
4-;5)
3
?
N
?
? =9 T .
39 (; ∓ .4)3 ((; ;3.=)
+
Ts N^
∓
Ts N^
?
3B 3B
?
? ;9
K.
39 39(.4) / ( 399, 999) + 3 (; ∓ .4) (; (;3.=) 3(;9)(;9) ∓4
? 6.9
K.
9.4 ∓4
SGd ;3 ;3.= .=(>9 (>9)( )(;9 ;9)) (3 (399 99,999 ,999)) T ` =9 L` ? ? ? >.9 K. S ;3.=
? 9.4%
? ;7 K.
Ljnugt`r gurrmjt1 (smm Mxkopbm 3-5)
?
L B,ros
L
3 B
3
∄ L / 3 + B ö ? 7
;9
3
+
>.4;/ >.4;/ 3
3
ö ? ;9.9< 7
K.
Gkpkglt`r gurrmjt1 (nmdljm t?9 kt pmkh gurrmjt) gurrmjt)
;9 ½ s
L G ,ros
? ; ∓4 3=(;9)
;/3
3= ½ s
∨ (∓>.>.4;(;9) t + 5.7) nt + ∨ (∓>)>) nt öö =
3
9
3
? >.5 ½ D , S ? =9 ℤ, t`j ? 9.4^ ?
9.4 3=999
? 3> ½ s
v` (t ) ? T`,okx m ∓ t / SG v` ( 3> ½ s ) ? T`,okx m ∓3>/X(=9)(>5)_
? T`,ok x ( 9.)
Ljnugt`r gurrmjt1 (smm Mxkopbm 3-5)
3
L B ,ros
?
L
3 B
∄ L / 3 + B ö ? 7
>.=
3
+
7.4 / 3
3
?
ö
7
>.43 K.
Gkpkglt`r gurrmjt1 D`r g`jvmjlmjgm, rmnmdljm t ? 9 kt tem pmkh gurrmjt. ^em gurrmjt ls temj mxprmssmn ks
? >.= ∓ ;.5 ( ;94 ) t
lG ( t )
d`r 9 2 t 2 3 ½ s
K
? ∓;.5 K L ros
;
d`r 3 ½ s 2 t
^
l (t )nt ^ ∨
?
3
^
?
9
; d
;
?
; 3 s >.= ∓ ;.5 ( ;9∓4 ) L G ,ros ? ∓4 ∨ =(;9) 9 ½
399,999
3
2 =½ s
? = ( ;9∓4 ) ? = ½ s
nt + ∨ (∓;.5) 3 ntö ö 3 s = ½ s
;/3
? 3.79
K.
½
4-3=) k ) Dr`o Mq. 4->5, N ? L B
?
T s N S (; ∓ N ) 3
?
T ` T s
+ T `
3>(.4) ;9(; ∓ .4)3
?<
∄ L B ? 3(< ∓ 7.4) ? ;9.5 Dr`o Mq. 4-35, B ?
? K.
74 3> + 74
⇓
T s N^
∄ L B
?
3>(.4) ;9.5(;99,999)
T `
? S ∄T ` T ö `
T s
+ T `
?
? 9.>(9 + =9
? ;7.7 ½ E 9.4
d
? ;9(9.99=)(;99,999) ? ;39 ½ D
4-34) Mxkopbm nmslfj1 ]sljf Mq. (4->5), N ?
L B,olj
K.
N c) Dr`o Mq. 4-74, G
? 9.4
? 9.==4
]slj ]sljf f Mq Mq.. (4 (4-> ->; ½ E). K g`oo g`oo`j `j prkgtlgm prkgtlgm ls t` smbm smbmgt gt B suge tekt Ge``sm B kt bmkst 3=% bkr ∄l B ? >9% `d L B ? 9.>9 ( 7.76= ) ? ;.7= K. ]sljf Mq. (4->=), B ?
T s N
∄l B d
?
>9 ( 9.==4 ) ;.7= ;.7= ( ;9 ;99 9, 99 999 9) G ?
]sljf Mq. (4-=>),
? ;4= ½ E N
?
∄T ` S ö T `
d
9.==4 77.7 ( 9.9;) ( ;99,999 ,999 )
? ;4.6 ½ D
4-36) Mxkopbm nmslfj1
]sljf Mq. (4->5), N ?
kjn N ?
;= ;5 + ;=
T ` T s
+ T `
, N?
;= ;3 + ;=
? 9.==4 d`r tem ;3-T s`urgm,
? 9.>== d`r tem ;5-T s`urgm. 3
]sljf Bolj
?
( ; ∓ N ) S 3 d
, tem w`rst gksm ls d`r N ? 9.>== d`r tem ;5-T s`urgm. 3
Bmtt Bmttlj ljf f d ? ;9 ;99 9 hEz hEz (nmslfjmr' mslfjmr'ss ge`lgm), Bolj
( ; ∓ 9.>== ) ;= ? ? 33.7 ½ E 3 ( ;99,999 ,999 )
Ge``sm Ge` `sm B kt bmkst bmkst 3=% bkrfm bkrfmrr tekj tekj B olj (35 ½ E) E).. Kbtmrjk Kbt mrjktlv tlvmby mby,, k g`oo`j g`oo`j prkgtlgm prkgtlgm ls t` smbmgt smbmgt B suge tekt ∄l B ? >9% `d L B . L b ?
T `3 T s SN
?
;=3 ;5 ( ;= ) ( 9.>== )
∄l B ? 9.>9 ( ;.57) ? 9.67
? ;.57
K
K. ]sljf Mq. (4->=),
B ?
T s N
∄l B d
?
;5 ( 9.>== ) 9.67 9.67 ( ;9 ;99 9, 99 999 9)
]sljf Mq. (4-=>),
G
?
G ?
9.==4 ;= ( 9.9;) ( ;99, 99 999 )
? ;;3 ½ E N
(;99
½ E wlbb
cm dljm)
, s` cksm G `j N ? 9.==4, (;3-T s`urgm)1
∄T ` S ö T `
d
? 76 ½ D
4-35) ]sljf tem mquktl`js T `
N ?
S ?
+ T `
T s
T `3 Y 3
?
Bolj
L B
?
( ; ∓ N ) S 3 d
Y T s N N
G ?
∄T ` ö T `
S
d
kjn usljf d ? ;99 hEz (nmslfjmr“s ge`lgm), rmsubts krm se`wj lj tem tkcbm.
Ts, (T)
Y (V)
N
S (ℤ)
Bolj (½ (½E)
LB ( (K K)
G (½D)
;9
;9
9.=>=
;>.>
;>.<
;.57
76.<
;9 ;> ;>
;= ;9 ;=
9.=>= 9.>43 9.>43
.> T kjn Y ? ;9 V, wemrm B olj ? 39.< ½E. Wmbmgt tem vkbum `d B kt bmkst 3=% bkrfmr tekj B olj (34.; ½D). ]sljf kj`temr g`oo`j grltmrl`j `d ΞlB ? >9% `d LB, kfklj d`r ;> T kjn ;9 V, B ? ;9> ½E. ^em vkbum `d G ls =4.5 =4. 5 ½D d`r tem w`rst gksm `d Ts ? ;9 T kjn Y ? ;9 V. V.
4-3
K.
39
T s
∄l B; ?
T s N B; d
⇓
B;
∄l B3 ? T s N ⇓
?
B3
B3 d
Ts N
∄l B; d
?
?
Ts N ∄l B 3 d
39(9.777) 9.;9(.=)(;99,999)
?
? ;.77 oE
39(9.777) ? 9.446 oE 9.;9(;)(;99,999)
4-7;) Mxkopbm nmslfj1 T ` T s L B 3
?∓ ?
L B; ?
N
;∓ N
Y`
?
∓T`
Y s T s
?
? 49 79
49 3=
∓79 3=
? ∓;.3 ⇓
N ? 9.=>==
? 3.9 K8 ⇓ ∄lB 3 ? 9.>(3.9) ? 9.> K ⇓
? 3.> K8 ⇓ ∄lB; ? 9.>(3.>) ? 9.>5 K ⇓
B3
≭
B; ≭
Ts N
∄lB 3 d Ts N
∄lB; d
? ?
Bmt d ? ;99 hEz (nmslfjmr's ge`lgm). ; ∓ N G3
; ∓ 9.=>==
≭ ∄T ` 5 B d 3 ? ( 9.9;) 5 ( 7 >;( ;9∓4 ) ) ( ;99, 999 ) 3 ? ;.46 ½ D T ö 3 `
TG; ? Ts
∓ T` ? 3= 3= ∓ ( ∓79 ) ? == T ⇓ ∄vG; ? 9.9 = ( == ) ? 3.6= T 3
]sljf S ? T`3 / Y ? ( ∓79 ) / 49 ? ;= ℤ, G; ≭
T` N Sd ∄vG ;
?
79 ( 9.= .=>= >== =) ;= ( ;99,99 ,999 9 ) 3.6= .6=
? 7. >>=) 9.> ( ;99, 999 ) 3= ( 9. 9.= =>> >>= =) 9.>5 ( ;99, 999 )
? 7>; ½ D ? 35> ½ D
4-73)
N?
T`
?
T` + Ts
L B; ?
T` 3 Ts S
?
;3 ;3 + =
;33 =(>)
? 9.694
? 6.3 K
∄l B; ?
Ts N B;d
L B;,okx
? 6.3 +
7.=7 ? 5.>K
3
?
;3 >
∄l B; ?
Ts N
?
L B3, okx
? 7+
L B3
?
T` S
B3d
? 7K (=)(9.694) 39 39((;9 ;9))-4 (;9 ;99 9,999) ,999)
;.64= ? 7.55K 3
? ;.64=K
;.64=
? 7∓
L B3,olj
3
? 3.;3K
4-77) T`
?
L B; ?
Ts N
?
;∓ N T` 3 Ts S
?
7.7(.6) ; ∓ .6 .6 6.6 3 7.7(=)
? 6.6T
? 7.4K
∄l B; ?
Ts N
L B;,okx
? 7.4 +
L B;,olj
3.4>K ? 7.4 ∓ ;.(;9 >(;9))-4 (799 (799,99 ,999 9) ;. +
B 3 d
?
? ;..=4K
? ;.=>K (7.7)(9.6)
;9( ;9(;9) ;9)-4 (799 799,999) 9.66 3
? ;. ∓
9.66 3
? ;.;==K
∄TG; ? ∄TG3 ? T` N ?
(6.6)(.6) =(=9 =(=9)( )(;9 ;9)) ∓4 (7 (799 99,999 ,999))
SGd
? 9.96;) Mquktl`j (4-4(;.3)3=9, 999
T` S
Ts N ( ∄l B3 )d
4 3
? ? 7K (;=)(9.354)
?
9.>(7)3=9, 999
? ;>.7½E
? T` ? 4
∄TG 3 ? ∄T` ? G; ? G3
T` N `r G3 SG3d
?
N
∄T` S ö d T`
?
9.354 3(.93)3=9,999
? 35.4½D
4-74)
T`
N?
S
?
T` + Ts 3.6 ;
L B; ? B; ?
?
3.6 3.6 + <
? 9.37;
? 3.6ℤ
T` 3 Ts S
?
3.6 3 .3½E
4-76)
∄lG ? L B,okx ? 3.6 K. ∄T ? ∄l r ? (3.6)(9.4) ? ;.43 T .
? =6.6½E
? 35.4½D
@ , MWS
G G
∄T @,MWS T @
?
;.43 79
V`rst gksm 1
? 9.9=> ? =.>%
4.>% ;.5 T` ? Ts 4ö ∓ 5 B ö 5( >9999 9999 ∾ ;5 ≮ T` ≮ 3;.> T . (; ∓ N) S (; ∓ 9.76=)(39) ? ? 4.3= g) Bd olj ? 3 Ljgrmksm Bd olj 1 m.f ., Bolj
?
3 4.3= >9999
? ;=6 ½ E
`r d olj
?
4.3= .; hEz
4->9) k)
Sokx ?
3 Bd N(; ∓ N) 3
?
3(;39)(;9) ∓4 ( 3=999) 9.4(;∓).4) 3
? 43.= ℤ d`r g`jtlju`us gurrmjt
c) D`r S?;99ά, temgurrmjt ls nls nlsg`jtlj g`jtlju`us1 u`us1
3 N 3 S^ ;+ ;+ ö B ö T` ? T s ö 3 ö 3(.4)3 (;99) / 3=999 ;+ ;+ ö ∓4 ;39(;9) ö ? 74 T . T` ? ;3 ö 3 öö ∾ 79 ≮ T ` ≮ 7 4 d` d `r 3= ≮ S ≮ ;99 g ) Bd olj
? >.5 ⇓
B
:
>.5 3=999
? ;.5 ;39(;9) ∓4
? >9 hEz.
4->;) Nlsg`jtlju`us d`rtem temswltge cugh-c``st Bmt N^ tlom tlom tekt tem swltge ls gb`smn kjn N;^ cm tem gurrmjt tlom tekt tlom ls `pmjg`jvmrtmr1 kjn tem gurrmjt ljcm temtem ljnugt`r ls p`sltlvm. D`r k b`ssbmss g`jvmrtmr, tem `utput p`wmr ls tem skom ks tem ljput p`wmr. Y s
L N ? Ts L s ? T s okx ö 3
L okx Y s ? Y ` ?
?
T s N^ B 3 s
T N 3^
3 B 3 `
T
S T s3 N 3^
3 B T ` T s
? N
?
T`3 S
S^
3B
4->3) Vemj swltgems ‒;‟ krm gb`smn, G ; kjn G3 krm g`jjmgtmn lj smrlms, mkge ekvljf Ts/3 v`bts.
Vemj tem ‒;‟ swltgems krm `pmjmn kjn tem ‒3‟ swltgems krm gb`smn, T` ? Ts `d tem s`urgm pbus Ts/3 `d G;, okhljf T` ? ;.=Ts.
4->7)
39 V p(t) d`r tem O@WDM^
;9 V
9V (;.999o,>9=.;9= oV -;9V 9. ? ;4.< T .
`
s
k) T
T `3
c) L Bo
?
∄l Bo ?
T s N
Bo d
?
L Bo,okx
? L Bo +
L Bo,olj
? L Bo ∓
g)
∄
3
>.=(9.4)(4)
? 6.97 K.
>.=(9.4) ;9( ;9(;9) ;9) ∓4 (3=9 (3=9,999 ,999))
∄l Bo 3 ∄l Bo 3
? 6.=6
K.
? 4.><
K.
? ;.95
K.
(9.4)
N
T `
?
T s NS
(;4.= T s N >> .73
? 4.>(9.73)(;)
? 9.4>9
∄l Bo ? 9.> L Bo ? 9.>(9.4>9) ? 9.3=4 Bo
?
T s N
∄l Bo d
?
>>(9.73) (9.3=4)(799,999)
K.
K.
? ;5> ½ E .
6->) Mxkopbm nmslfj
? 3> T . Y` ? >9 V . J 3 T ` ; ∓ N ? ö J; T s N Bmt N ? 9.> (krcltrkry ) T s
T`
? >9 T .
temj J 3
?
>9 ; ∓ 9.>
J
? 3.=, `r ; ? 9.> ö J J 3> 9.> ; 3 T J >9 3 ` ? L Bo ? ( 3.=) ? >.;6 ö (; ∓ N ) S J ; (; ∓ 9.>)>9 3
wemrm S ? Bmt ∄l Bo
G
? >9 ℤ
Y >9 ? >9% `d L Bo
T s N
?
?
>93
? 9.>(>.;4) ? ;.46
K
? ;99 hEz
Bmt d Bo
T `
K
∄l Bo d
?
3>(9.>) ;.46(;99,999)
N
?
9.>
?
S ∄T `ö d T `
? =6.4 ½ E ? 39 ½ D
>9(.99=)(;99,999)
6-=) D`r g`jtlju`us g`jtlju`us gurrmjt
L Bo,olj
? L Bo ∓
∄l Bo 3 3
L Bo,olj
?9?
T`
T s NS
3
S ?
T` 3 Bo d (T s N )
S ≮ ;;.6
3
?
ℤ ⇓ S : ;;.6 ℤ ⇓
∓
Ts N 3 Bo d
=3 (3) (3)(=99)(;9∓4 )> )>9 9,999 ,999 3
X 3>(9.75=)_
g`jtlju`us gurrmjt nlsg`jtlju`us gurrmjt
? ;;.6 ℤ
6-4) Wwltge ls gb`smn gb`smn d`r N^, N^, gurrmjt rmturjs t` zmr` kt t ? tx1
L Bo,okx
?
T s N^ Bo
Wwltge `pmj 1
nl Bo nt
∓T J ? ` ;ö Bo J 3
; ∓T` J; t ∓T` J Ts N^ + ? ∓ + l Bo (t ) ? n l N ^ t N ^ θ ( ) ( ) ö ö Bo ∨ Bo J 3 N^ Bo J Bo 3 T N^ ∓T` J ; (t x ∓ N^ ) + s ö Bo J 3 Bo
L BO (t ? t x ) ? 9 ? t x
?
T s N^ J 3
J ö + N^ ;
T`
6-6)
k ) T`
∄T ` T`
J ? Ts N 3ö ? ;99(.7=)(;) ? 7= T . J ; ;∓ N ; ∓ .7= ? ? ∓4 ∓4 3
c) L Bx
5(69)(;9) 77(;9) (;=9, 999) 3
5 BxGd
?
T ` S
?
7= 39
? ;.6=
J ∄l Bx ? Ts 3ö ∓ T` J; L Bx ,okx L Bx ,olj g)
? ;.6= + ? ;.6= ∓
∄l Bo ?
3.;6 3 3.;6
T s N^ Bo
3
?
? 9.;4%
K. N
B x d
? X;99(;) ∓ 7=_
.7= 4
(6 (69) 9)((;9) ;9) ∓ (;= ;=9,99 9,999) 9)
? 3.57 K. ? 9.46
K.
;99(.7=) 7
;(;9) ;9) ∓ ;=9 ;=9,999
9.377 K.
? L; + lBo ? l prl L sw,okx ? L Bx, okx (; / ;) + L Bo ,okx ? 3.57 + 9.377 ? 7.94 n ) l sw
K.
? 3.;6
K.
6-5)
k ) T`
∄T ` T`
3 ;ö ? Ts N J ö ? ;6 9(9.7) ;9 ? =.; T . J ; ;∓ N ; ∓ 9.7 ? ? ∓4 ∓4 3
5Bx Gd
5( 39)(;9) ;9(;9) (=99, 999) 3
? 9.;6=%
c) ^em gurrmjts lj tem g`jvmrtmr krm se`wj cmb`w. ^em wljnljf gurrmjts krm d`r tem wljnljfs lj tem lnmkb trkjsd`romr o`nmb, j`t tem peyslgkb wljnljfs. ^em peyslgkb prlokry wljnljf gurrmjt ls tem suo `d wljnljf #; kjn B o gurrmjts.
g)
s ;69(9.7) N^ ? ∄l Bo ? T B ? 9.7 4 7>9( 7>9(;9 ;9)) ∓ =99 =99,999
K.
o
Ymkh mjmrfy lj Bo 1 Vokx Y ?
V ^
?
; 3
Bo ( ∄lBo )
3
?
; 3
4
(7>9)(;9) ∓ (9.7)
3
? ;=.7 ½ A
? Vd ? ;=.7(;9)∓4 (=99, 99 999) ? 6.4= V .
6-5 (j`t ujlqum)
Bd L Bx,olj
c)
? =∓
7.= 3
;99( ;99(;9 ;9)) ;99 ;99,999
? 7.3= K. : 9 ∾ g`jtlju`us gurrmjt
∄T ` ; ∓ N ; ∓ 9.7 T` ? 5 Bx Gd 3 ? 5(; 99)(;9) ∓4;=9(;9) ∓4 (;99, 999) 3 ? 9.9=5%
6-;9)
J ; ? Ts N 3ö ? ;99 (9.3=) ö ? = T . = J ; usljf B x ? 39 ½ E , ∄T ` ; ∓ N ; ∓ 9.3= ? ? 3 ∓4 ∓4 k ) T`
T`
5Bx Gd
5( 39)(;9) ;9(;9) (76=, 999) 3
? 9.77%
c) ^em gurrmjts lj tem g`jvmrtmr krm se`wj cmb`w. ^em wljnljf gurrmjts krm d`r tem wljnljfs lj tem lnmkb trkjsd`romr o`nmb, j`t tem peyslgkb wljnljfs. ^em peyslgkb prlokry wljnljf gurrmjt ls tem suo `d wljnljf #; kjn B o gurrmjts.
g)
∄l Bo ?
T s N^ Bo
?
;99(9.3=)
Ymkh mjmrfy lj Bo 1 Vokx Y ?
V ^
∓4
777 777(;9) ;9) 76= 76=,999 ; 3
9.39 K.
Bo ( ∄lBo )
3
?
; 3
∓4
(777)(;9) (9.3)
? Vd ? 4.44(;9) ∓4 (76=, 99 999) ? 3.= V .
3
? 4.44 ½ A
6-;;)
k ) T`
? Ts N J 3ö ⇓ J ö; ? T s N ? ;3=(9.7) ? 9.6= T ` =9 J; J 3
c) L Bx
?
∄l Bx ? g)
T `
?
=9
?3
S 3= T` (; ∓ N)^ B x
∄T ` ; ∓ N ? 3 T`
5 Bx Gd
K.8 L Bx,olj
⇓
?
? (9.>)(3) ? 9.5
K.8
∄lBx ? 3(3 ∓ 9.5) ? 3.>
K.
T` (; ∓ N )^ =9(; ∓ 9.7)
? ? =5.7 ½ E . ∄lBx 3.>(3=9,999) ; ∓ 9.7 ;∓ N ? ? >.5 ½ D . ⇓ G ? ∓4 5(=5.7)( )(;9) ;9) (9.99= (9.99=)(3= )(3=9,999) 9,999)3 ∄T ` 3 5(=5.7 5 B x ö d T ` Bx
6-;3)
Bmt
J ; J 7
? ;, temj N 2 9.=
Bmt N ? 9.7=, temj J ; J 3
?
T s N T `
?
(;69)(.7=) >5
J S`ujnljf , bmt ; J 3 ^emj N ?
? ;.375 (;.3=) ? 9.7=7 ö ö T s J 3 ;69
Bmt d ? 399 hEz, kjn nmslfj d`r ∄l Bx ? >9% `d L Bx T (; ∓ N) >5(; ∓ 9.7= 7=7 7) ? ;3> ½ E ? B x ? ` 9.> L Bx d 9.>(7.;3=)399,999 wemrm L Bx
? L` ?
Y ` T `
?
;=9 >5
? 7.;3=
K.
Kbtmrjktlvmby, s`bvljf d`r tem oljlouo B x d`r g`jtlju`us gurrmjt ,
∄l Bx
T`
T` (; ∓ N)
L Bx ,olj
? 9 ? L Bx ∓
B x ,olj
?
(; ∓ N ) S 3 d
wemrm S ?
T `3
?
Y `
?
3
?
S
∓
3 B x d
(; ∓ 9.7=7)(;=.74) 3(399, 999)
>53 ;=9
? 3>.< ½ E
? ;=.74 ℤ
B x oust cm frmktmr tekj 3>.< ½ E wlte okrflj, (m.f ., 3=% frmktmr ) okhljf B x
≭ 7; ½ E
? ;3> ½ E , ; ∓ N ; ∓ 9.7=7 ? ? ;.47 ½ D G: 4 3 5(;3>)( )(;9) ;9)∓ (9.9; (9.9;)(39 )(399,999) 9,999) ∄T ` 3 5(;3> 5 B x ö d T `
]sljf B x
6-;7)
;=9 ≮ T s
≮ ;6= T .
? 79 T . 39 ≮ Y` ≮ =9 V ⇓
T`
9.446 ≮ L `
≮ ;.446
K.
Mxkopbm nmslfj n mslfj 1 Bmt
J ; J 7
? ;, temj N 2 9.=
Bmt N ? 9.7 d`r T s ^emj
J ; J 3
D`r T s
?
T s N T `
? ;6=
?
? ;=9 T .
(;=9)(9.7) 79
? ;.=
T ., N ? T ` J ;ö T s J 3
? 79ö (;.=) ? 9.7= ;6=
∾ 9.7 ≮ N ≮ 9.7=, ggmptkc ptkcbm bm rkjfm rkjfm `d N. @temr @temr ge`l ge`lgms gms krm p`sslcb p`sslcbmm. welge ls kj k ggm ]sljf tem nmslfj grltmrl`j `d B x
?
T` (; ∓ N) 9.> L Bx d
∄l Bx ? >9% `d
L Bx ,
Bx
^em w`rst gksm ls d`r tem sokbbmst sokbbmst N kjn tem te m sokbbmst L Bx .
? 3=9 hEz (krcltrkry ), 79 79((; ∓ 9.7) 9.7) B x ? 9.>(9.446)(3=9,999) ? 7;= ½ E ; ∓ N ; ∓ 9.7 ? ? 3.33 ½ D G: 4 3 5(7;=)( )(;9) ;9)∓ (9.993)(3=9, (9.993)(3=9, 999) ∄T ` 3 5(7;= 5 B x ö d T `
Bmttljf d
6-;>) ^em gurrmjt lj tem peyslgkb prlokry wljnljf ls tem suo `d l B; kjn lBo lj tem o`nmb. ^em peyslgkb gurrmjts lj wljnljfs 3 kjn 7 krm tem skom ks lj tem o`nmb.
6-;=)
k ) T`
J ? 3Ts söö N ? 3(=9)(9.=)(9.7=) ? ;6.= T . J p
c) L Bx
?
∄l Bx
T `
?
;6.=
? 3.;< T .
S 5 T ? ` (9.= ∓ N)^ B x
L Bx,okx
? L Bx +
∄l Bx 3 ∄l Bx
?
;6.= 49(;9)∓4
? 3.;< +
9.3< 3 9.3<
(9.= ∓ 9.7=);=9, 999 ? 9.3< K.
? 3.77 K.
L Bx,olj ? L Bx ∓ 3 ? 3.;< ∓ 3 ? 3.9> K. ∄T ` ; ∓ 3 N ; ∓ 3(9.7=) ? ? g) T ` 73 B xGd 3 73( 49)(;9) ∓4 7(;9)
? ;.33
K.
J ? 3Ts pö ? 3(3>)(3) ? 9
43.=8 L Bx
?
T `3 Ts S
?
=9
3
79(43.=)
? ;.77 K.
6-3;)
? Y ` T s L Bx ? T` L `
Y s
J 3 (; ∓ N)^ ? L ` ? L Bx pö ö J s ^ J p T s L Bx ? T` L Bx ö 3(; ∓ N) J n J ; ∾T` ? T s W öö ö J p 3 (; ∓ N)
L x
6-33) ^em sloubktl`j ls ruj usljf k ^rkjslmjt Kjkbysls Kjkbysls wlte k rmstrlgtmn tlom `d 7 t` 7.93 os, rmprmsmjtljf tw` pmrl`ns `d stmkny-stktm `pmrktl`j. ^em stmkny-stktm `utput v`btkfm eks kj kvmrkfm vkbum `d kppr`xloktmby 79 T kjn pmkh-t`-pmkh rlppbm `d kppr`xloktmby 499 oT, lfj`rljf tem jmfktlvm splhm. ^em kvmrkfm trkjsd`romr prlokry kjn smg`jnkry gurrmjts krm ;o,79.3;o,34 K, 9.o,;.>>47)
WMB:: 9K
(7.4354o,o,;.=945)
9K
(7.4356o,497.779o)
-3.9K L(B;)
3.9K (7.4;;>o,;.>>47)
9K
(7.4356o,6o)
-3.9K ;.9K 9K
-L(B3) (7.4;;=o,=7os
7.4=os
7 .4 4 o s
6-3>) Nmslfj d`r εg`? -3;9¹ kjn k fklj `d 39 nC d`r k gr`ss `vmr drmqumjgy `d ;3 hEz.
Dr`o Mq. 6 ∓ 5=, H
ό z ?
ό g` H
?
D`r fklj Bmt S; G;
?
6=>99 7.67
? 7.67 1
? 3ω ;3999 ? 6=>99 rknls
όg`
? 39399 rkn / s
? 39 nC,
S3 S;
? ;9
? ; h ℤ, S3 ? ;9 h ℤ ;
S3ό z
? >.=¹ ∓ (∓;9=¹) ? ;=9¹ ε g`op ;=9¹ ? tkj ö ? 7.67 H ? tkj ö 3 3 Fklj ? ;= nC + .= nC F ? ;9 3>.=/39 ? ;4.5 ε g`op
S3 S;
? ;4.5
Bmt S;
? ; h ℤ kjn
? ;4.5 h ℤ 7.67
H
6-34)
S3
G;
? 3ω d g` S3 ? 3ω (=999)(;4, 599) ? 6.96 jD
G 3
?
; H 3ω d g` S3
?
; 7.67(3ω =999)(;4, 599)
? =95 =95 pD
]sljf Ts ? 4 T ks lj Mxkopbm 6-5, tem drmqumjgy rmsp`jsm `d tem `pmj-b``p systmo se`ws tekt tem gr`ss`vmr drmqumjgy ls kppr`xloktmby ;4.5 hEz. ^em peksm kjfbm kt tem gr`ss`vmr drmqumjgy ls ;6¹, welge ls ouge bmss tekj tem nmslrmn vkbum `d kt bmkst >=¹. ^emrmd`rm, tem systmo n`ms j`t ekvm tem nmslrmn nmfrmm `d stkclblty.
;3 9 Yeksm 59
>9
Okfjltunm (nC) (;4.5;>H,;4.544) (;4.5;>H,>5.>7 9 ;9Ez ; 99 E z N C (T (T ( m r r ` r ) ) Y ( T (m (m r r `r `r ) )
; .9 H E z Drmqumjgy
;9HEz
; 99 H E z
6-36) k) K drmqumjgy rmsp`jsm `d tem glrgult ylmbns T ` ≅ -3.= nC kjn ε ≅ ;97¹ kt ;9 hEz.
>9 Okfjltunm
-9
(;9.999H,-3.=;5;)
Yeksm
-> 9
-5 9
-;39 ;.9Ez
(;9.999H,-;93.4>4)
; 9E z
;99Ez
;.9HEz
;9HEz
;99HEz
N C ( T ( @ ut ut p u t ) )
Y ( T ( @ u tp tp u t ) ) Drmqumjgy
c) Vlte Vlte T p ? 7, tem fklj `d tem YVO dujgtl`j ls 39b`f ;9(;/7) ? - nC. ^em rmqulrmn fklj `d tem g`opmjsktmn mrr`r kopbldlmr ls temj 3.= + ? ;3.94 nC, g`rrmsp`jnljf t` k fklj okfjltunm `d >.9. ^em peksm kjfbm `d tem g`opmjsktmn mrr`r kopbldlmr kt tem gr`ss`vmr drmqumjgy t` flvm k peksm okrflj `d >=¹ ls
ε g`op
? >=¹ ∓ (∓;97¹) ? ;>5¹
Dr`o 6-6=, 6-5=, 6-54, kjn 6-56,
Bm Bmtt S; ?;h ?;hά,te ά,temjS mjS 3 ? >hά.
ε g`op ;>5¹ ö ? tkj ö ? 7.>< 3 3
H ? tkj G; ?
G3
?
H 3ω d g` S3
?
; H 3ω d g` S3
7.>< 3ω (;9, 99 999)(>999)
?
? ;7.5 jD
; (7.>999)
? ;.;> jD
g) Smdmrrljf t` Mxkopbm 6-> nC, kjn tem peksm kjfbm ls -;99¹.
>9 Okfjltunm
(5.97=5H,-3.>7=5) -9
-> 9
Yeksm
(5.97=5H,-;99.;=4)
-5 9
-;39 ; .9 E z ;9Ez N C ( T ( @u @u t p u t ) )
;99Ez ;.9HEz Y (T (T ( @ ut ut p u t ) ) Drmqumjgy
;9HEz
;99HEz
c) ^els nmslfj ls d`r d g` g` ? 5 hEz. Vlte T p ? 7, tem fklj `d tem YVO dujgtl`j ls 39b`f ;9(;/7) ? - nC. ^em rmqulrmn fklj `d tem g`opmjsktmn mrr`r kopbldlmr ls temj 3.>> + ? ;;.=¹ ∓ (∓;99¹) ? ;>=¹
Dr`o 6-6=, 6-5=, 6-54, kjn 6-56,
Bm Bmtt S;?;hά,te ?;hά,temjS mjS 3 ?7.=¹ ∓ (∓;>9¹) ? ;5=¹ 3
;5=¹ + όg` ? 3ω d g` ? 3ω (;=, 999) ? , 3>5 rkn / s Bmt S; ? ; h ℤ S3
?
G;
?
F S; H H
ό g` S3
? 3.; L okx ? ;.9K
9K
->.9K
9s
>9 o s
59os
; 3 9 os
;49os
L(B)
^lom
5-7) k)
T ng S
?
;=9 39
? 6.= K.8
ώ
?
B S
?
>9 oE 39 ℤ
? 3 os8
^ 3ώ
; / 49
?
> os
]sljf ]slj f Mq (5 ∓ 5) 5),,
; ∓ m ∓>.;46 L okx ? 6.= ∓>.;46ö ? 6.36; K. ; + m L olj ? ∓ L okx ? ∓6. 6.36 36; ; K. ]sljf Mq. (5-=),
l`
c)
6.= ;>.5m ∓t /.993 ? ∓ ;/;39)/.993 ∓6. 993 6.= = + ;> ;>.5 .5m ∓ (t ∓;/;39)/.
d`r 9 ≮ t ≮ 5.77 os d`r 5.77 os
≮ t ≮ ;4.6 os
? >.;46
3 99 o s
g) L pmkh ? 6.36; K. n ) Tokx
? Tng ? ;=9 T .
5->)
k)
T ng S
? ;3= ? 4. 3= K.8
ώ
39
?
B S
? 3= oE ? ;.3= os8 39 ℤ
^ ? ; / 49 ? ;7.77 3ώ ;.3= os
]sljf ]slj f Mq (5 ∓ 5),
; ∓ m∓;7.77 ? 4.3= ∓;7.77ö ? 4.3= K. ; + m L olj ? ∓ L okx ? ∓4.3= K. L okx
]sljf Mq. (5-=),
4.3= ∓ ;3.=m∓t /.99;3= l` ? ∓ (t ∓;/;39)/.99;3= 4.3= = + ;3 ;3.= .=m ∓4.3
d`r 9 ≮ t ≮ 5.77 os d`r 5.77 os ≮ t ≮ ;4.6 os
c) ]sljf tem dlrst ekbd-pmrl`n, L ros
?
; ;39
;/;39
∨ ( 4.3= ∓ ;3.=m∓t /.99;3= ) 9
3
nt
? =.>= K.
3
3 g) Y ? L ros S ? ( =.3= ) 39 ? = V .
L s
?
Y T ng
?
= ;3=
? >.6= K.
5-=) k)
Q ; ? ;=3
T; ? L;Q;
?(5
T; ?
>T ng
⇓
ω
c)
3
Tj
?
3
+ 3ω ( >99 ) ( 9.9;) ? 3
8
Qj
?
S3
j ; 7 =
^EN L
; .9 .93 33
?
+ ( 3ω >99 B ) 3
Tj 77; ;;9 44
+ 9.76 .76 3
5.9
8
Lj
?
Tj Q j
Qj 3T ng ω
c) Tj
?
3
⇓ >Tng jω
+ 3ω ( ;39 ) ( 9.93=) 3 ? 7;.7 ℤ
8
) ( 7;.7) ? 55.4 T . Tng
?
T
ω ;
? 4 Qj
?
S3
+ ( 3ω ;39 B ) 3
8
Lj
?
Tj Q j
8 L j ,ros ?
j
Tj
Qj
Lj,ros
; 7 =
55.4 33 + 9.;73 3.9
? 9.;5 9.;5= = ? ;5 ;5.=% .=%
L j 3
D@]SLMS G@OY@JMJ^W @D ^SKJWLMJ^ SMWY@JWM L(BPB) NG G@OY@JMJ^ ? -7.445695M-94 EKSO@JLG DSM[]MJG\ D@]SLMS J@SOKBLQMN YEKWM J@SOKBLQMN J@ (EQ) G@OY@JMJ^ G@OY@JMJ^ (NMF) YEKWM (NMF)
; 3 7 > =
;.399M+93 3.>99M+93 7.499M+93 >.599M+93 4.999M+93
3.579M+99 =.766M-94 >.665M-9; 7.=5.>
-; 9
7 9os L ( S)
7 = os T( K)/ ;9 9
> 9os
> =o s
=9 os
^lom
5-5) k ) T ;
λ
Tj
?
>T ng ω
ö g`s ( λ )
> ; 3 = T ( ) ng ?
>Tng
ö g`s ( jλ ) jω
8
Qj
?
?
Tj Q j
8 L j ,ro s
?
j ; 7
|Tj| .6
Lj,ros =.95 ;.=
=
>.>7
7<
9.95
^EN L
5- ( 399 ) ω
? ;9 +
? 3== T .
a 3ω 49 ( 9.97= )
? ;4.4 ℤ
3==
? Q ; ? ;4.4 ? ;=.7 K. ;=.7
L;,ros
?
c)
Kt 79 Ez ,
3
? ;9.<
K.
Q; ? ;9 + a 3ω 79 ( 9.97= ) T; ? L;Q; ? ( ;=.7) ( ; 3. 3.9 )
>T ng g`s λ ö ( ) ω
T ; ?
? ;3.9 ℤ
? ;5> T .
⇓
λ
T ω ;5>ω ? g`s∓; ; ö ? g`s∓; ö ? >7.6¹ >T ng > ( 399 )ö
5-;9)
λ ? 79¹ ]sljf tem DD^ dujgtl`j lj Yr`cm se`ws tekt v`btkfms kt drmqumjglms kt oubtlpbms `d j ? 7 krm kcsmjt.
c) λ ? ;=¹ ]sljf tem DD^ dujgtl`j lj Yr`cm se`ws tekt v`btkfms kt drmqumjglms kt oubtlpbms `d j ? = krm
kcsmjt.
5-;;)
Dr`o Mq. (5-33), λ
?
3 ;=9 3 Tros ? To nt + To nt + To ntöö 749 79 44 ;34 ; 79 ) + ( ;;> ∓ 44 44 ) + ( ;=9 ∓ ;34 ) ? 9.679T o Tros ? To ( => ∓ 79 3
∨
∨
∨
;59
5-;7)
^em TYVBPDLBM s`urgm ls g`jvmjlmjt g`jvmjlmjt d`r tels sloubktl`j. K pmrl`n `d 749 smg`jns ls usmn, okhljf mkge smg`jn mqukb t` `jm nmfrmm. K trkjslmjt sloubktl`j sloubktl`j wlte k ruj tlom `d 749 smg`jn kjn k okxlouo stmp slzm `d ;o flvms f``n rmsubts. ^em DD^ `d tem Yr`cm `utput g`jdlros tekt tem 7rn kjn =te ekro`jlgs kjn temlr oubtlpbms krm mbloljktmn. 9 79 79.9; => =>.9; 44 44.9;
9 9 ; ; 9 9 ;
;;> ;;>.9; ;34 ;34.9; ;=9 ;=9.9; 3;9
; 9 9 ; ; 9 9
3;9.9; 37> 37>.9; 3>4 3>4.9;
-; -; 9 9 -;
3 3.9; 794 794.9; 779 779 749
-; 9 9 -; -; 9 9
5-;>)
k)
c) Tng
To
?
? >5 T 8
>T ng jω
λ;
g`s ( jλ; ) + g`s ( jλ 3 ) + g `s ( jλ 7 )
? ;=¹ 8 λ 3 ? 3=¹
8
λ 7
? ==¹
; ;>
? 9.5;=
5-;=) ^` mbloljktm tem telrn ekro`jlg, g`s(7λ; ) + g`s(7λ 3 ) + g`s(7λ 7 ) ? 9 Wmbmgt tw` `d tem kjfbms kjn s`bvm d`r tem telrn. Mxkopbms1 λ; ;= 39 ;9 ;9
λ3 3= 79 79 79
λ7 == >9 =9 69
Ol 9.5;= 9.5=6 9.57; 9.67;
< -;>.>
5-;4) ^els ljvmrtmr ls nmslfjmn t` mbloljktm ekro`jlgs j ? =, 6, ;;, kjn ;7. ^em j`rokblzmn g`mddlglmjts ter`ufe j ? ;6 krm j Tj/Tng ; >.>=7 ≅ 9 ;7 -9.9965 ≅ 9 ;= -9.9769 ;6 9.;63= ^em g`mddlglmjts krm j`t mxkgtby zmr` d`r te`sm ekro`jlgs cmgkusm `d r`ujnljf `d tem kjfbm vkbums.
5-;6)
5-;5) T; ? T;,ros 3 ok
?
Q j
?
T ; T ng
?
? =>
64.5 )
? 73 +
aj> > ? >.>% >.>% ? 9.9>
3
5-39) ^em glrgult ‒Ljvmrtmr Clp`bkr YVO Dujgtl`j‟ ls sultkcbm t` vmrldy tem nmslfj rmsubts. ^em pkrkomtmrs krm o`nldlmn t` oktge oktge tem pr`cbmo vkbums.
^rkjslmjt Kjkbysls Kjkbysls kjn D`urlmr Kjkbysls Kjkbysls krm mstkcblse lj tem Wloubktl`j Wmtup omju1
^em `utput dlbm g`jtkljs tem ^EN `d tem b`kn gurrmjt, vmrldyljf tekt tem ^EN ls bmss tekj ;9%. ^@^KB ^@^K B EKSO@JLG NLW^@S^L@J ? T.
? ;4.>
? ;7.4
K.
Ge``sm `nn ljtmfmr ;< `r `r frmktmr d`r o d .
5-33) Mxkopbm s`butl`j1 T;
? T;,ros
Bmt ok
L;
?
T; Q;
^EN L
3
? 9.< ⇓
≅
?
o d :
3 ? ;>; T .
Tng
T ;
?
S + aό 9 B
L od L ;
Lod
2 9.;9
?
?
T ; ok
?
;>; 9.<
? ;=6 T .
;>; 7 9 + a 766 ( 9.93= )
⇓
? >.>5
L od 2 9.;( >.>5 )
K.
? 9.>>5
K.
9.6;( ;=6 )
T od Q od
? ;99
:
9.>>5
3>< 766 ( 9.93= )
? 3>< ℤ ≅ o d ό 9 B
? 34.>
Ge``sm `nn ljtmfmr 3< `r frmktmr frmktmr d`r d`r o d .
5-37) ]sm tem clp`bkr YVO dujgtl`j glrgult `d Dlf. 5-37k, kjn usm tem ujlp`bkr YVO dujgtl`j glrgult `d Dlf.5-34 wlte o d ? ? ;9. ]sm o k ? 9.5 d`r T ; ? ;39 T dr`o tem ;=9-T ng s`urgm.
^em ^EN d`r clp`bkr, o d ? 3;, ls ;9.3 %, d`r clp`bkr o d ? ? >; ls =.3%, kjn d`r ujlp`bkr o d ? ? ;9 ls =.;1
]jlp`bkr, od ? ? ;91
5-3>)
?
k) T;, B ∓ J
L;
?
T ; Q ;
L;,ros
7ω
ω 3ω =9 9 3 + g`s 7ö ∓ g`s 7ö ö ? 7ω ö
;=<
?
?
3T ng
?
3 = + a 766 ( 9.939 )
L ; 3
? >.7;
;=< 34.;
? 4.9<
7 ? ;=< T .
K.
K.
5-3=)
]sm Mq. (5->3) d`r Tj,B-J , Q j
? S+
aj3ω dB , L j
? Tj, B- J / Q j ,
kjn L j, ros
D`r d ? 3= Ez1 j ; = 6 ;; ;7
^EN L
?
.>;3 ;
TjB-J 3== =9.< 74.> 37.; ;.= =3.5 43.9
Lj 37.9 3.9 ;.94 9.>> 9.73
Lj,ros ;4.7 ;.>; 9.6= 9.7; 9.33
? 9. 9.;9 ;9 ? ;9 ;9% %
=9.3 + 9.333 + ; 37.; ;=
Lj ;;.< 9.=> 9.36 9.;3 9.95
+ 9.;7
Lj,ros 5.>7 9.75 9.;< 9.95 9.94
? 9. 9.9=; 9=;< < ? =.;(;9) 6
rkn / s
? 6.96 ℤ
? ;3 js
∓; T s slj ö + ω + t; ? 3>4 js ό 9 L ` Q 9 ;
Br L ` ό 9
X; ∓ g`s ό9 (t3 ∓ t; )_ + t3
? ;.96 ½ s
t ? Ts ; ∓ d s t7 ∓ ; ö ? =.4 T . 3 D`r L ` ? 5 K., t; ? ;= js, t3 ? 3=3 js, T`
t7
? 5 ½ s
? 4>=.> hEz
d s
7.; hEz
≮
d s
≮ 4>=.> hEz
9 ∓ ;= ? ? 4.3= ℤ >
Br ? Q 93G
⇓
G r ?
; Br ό 93 Br ?
Q 9 ό 9
?
4.3= ;.4(;9) 4
? 9.; ½ D . ? 9.76= ½ s
slj ∓;
T s
+ ω + t ? 3.6> ½ s
? 7..43 ½ s
; ∓ = / ;= ∓4
? ;=9 hEz .
( >.43 ∓ 9.76= / 3)(;9)
.6 ½ E
? 37.= jD .
) K sultkcbm glrgult ls se`wj. ^em vkbums `d tem `utput dlbtmr dlbtmr g`op`jmjts B; kjn G3 krm j`t grltlgkb. ^em b`kn rmslst`r ls ge`smj t` flvm ;9 K. ^em swltge oust cm `pmj d`r kj ljtmrvkb cmtwmmj t3 kjn t78 =9 js ls ge`smj.
>99u Mjmrfy dr`o s`urgm pmr pmrl`n (;>99u W(V(T;)) (;>69u,;39.;3=) ;99T Gkpkglt`r =9 T
@utput ;>.=65)
9T ;>us ;>.4 T., T., c) TG,pmkh ? ;39 T., g) Ljtmfrktm ljstkjtkjm`us p`wmr, flvljf 63.6 βA pmr pmrl`n (suppblmn). T ng
G
?
? =.44 ? 76.6
; [ό 9 S
? 55.< T .
Tng
2 (9.9=)(;;7) ? =.44 T .
D`r k squkrm wkvm, T7 T `,7 T l ,7
⇓
ω
?
T ; 7
?
;;7 7
7 ό9 ό 9 ∓ ö ό 9 7ό 9
; + [3
? ;7.> ½ D .
? 76.6 T
; 3
⇓
(ljput t` dlbtmr )
[ ? 3.>6
B ?
; 3
ό 9 G
T G , pmkh pmkh ?
? ;;.5 oE . T ;
ό 9 SG
? 359 T .8
L B, pmkh ?
T ; S
?
;;7 ;3
? 7 K.
;>; T . ? ⇓
T7
>T ng
?
T `,7
;
T l ,7
G
?
B ?
;>.; >6
[ό 9 S ; 3
ό 9 G
?
T ;
7 ό9
; + [3
;
Tng
? ;7.< ½ D .
ό 9
7
∓
?
;>; 7
ö 7ό 9
3
ό 9
? ;.36 oE .
39 9
;9 9
(;9.>;4o,7.43;3) 9
? ;;; T .
2 (9.;)(;>;) ? ;>.; T .
D`r k squkrm wkvm, T7
?
⇓
ω
? >6 T ⇓
(ljput t` dlbtmr ) [ ? ;.;<
-;99
-399 ;9.9os T(T;1+)
;9.>os T(@]^)
;9.5os L(S;)
;;.3os
;;.4os
;3.9os
^lom
^em `utput dlbm se`ws tekt tem ^EN llss ;9.6%. Ljgrmksm [ cy ljgrmksljf B, kjn knaust G kgg`rnljfby. B?;.> oE kjn G?;3.4 ½D flvms ^EN?4 T .
K.
;=
39 9
v(`ut) T(gkp)
;9 9 T(lj)
(;9.>7>o,5.;394) L(B) 9
-;99
-399 ;9.9os T(@]^)
;9.>os T(LJ)
;9.5os T(B;13,G;13)
;;.3os L(B;)
;;.4os
;3.9os
^lom
Dr`o tem `utput dlbm, ^EN ? ;9.5%. Dr`o Yr`cm1 TG,pmkh ?;>< ?;> < T. T.88 LB,pmkh ?5.;3 ?5.;3 K. ½ E .
9
G s
? Gp ?
; 3
ό 9 B
? ==.= jD .
Gemgh wlte Mq. < ∓ 6> 1 T` ? ;9.93 T . ]sljf k glrgult cksmn `j Dlf. > .>> βs kjn tem swltge oust rmoklj gb`smn d`r =.>= βs. ^em s`urgm p`wmr kjn kj n mjmrfy krm j`t gekjfmn slfjldlgkjtby. slfjldlgkjtby.
39
(39.u s T (W V L^ GE) T ( GK Y )
5us L( B ; )
; 3us
; 4 us
^lom
) ό `
λ
?
?
BrG r S
3 Br
?
?
; ∓4
3=9((;9 3=9 ;9)) 9.; 9.;(;9 ;9)) ;
3( 3=9)(;9) ∓4
∓4
? 3(;9)=
rkn / s
? 3999
∓ λ 3 ≅ ό9 vG (t ) ≅ Ts + m ∓ t X ∓Ts g`s ό`t + ό` Br ( L; ∓ L ` ) slj ό `t _ ? 6= + m∓3999t X∓6= g`s(3(;9)= t ) + 3(;9)= 3=9(;9) ∓4 (6 ∓ =) slj(3(;9)= t )_
ό
?
;
3
ό`
λ
slj( 3(;9) = t )_ 6= m ∓3999 t X 6= g`s( 3(;9)= t ) ;99 sl v?G (tx + ) ?9
⇓∓ t x ? 33.7 ½ s + T l B ( t ) ≅ L ` + m ∓ t ( L; ∓ L ` ) g `s ό`t + s slj ό `t ό ` Br 6= ? = + m∓3999t (6 ∓ =(g`s(3(;9)= t ) + λ
slj( 3(;9)= t )
3 9u s
3 > us
3(;9) 3(;9)= 3=9(;9) 3=9(;9) 4 ? = + m∓3999t 3 g`s(3(;9)= t ) + ;.= slj(3(;9)= t ) l B (t x ) ? lB ( 33.7 ½ s) ? 7.;> K. ∄l B Br (6 ∓ 7.; 7.;>)3= )3=9(;9 ;9)) ∓4 ∄t ? ? ? ;3.< ½ s T s
6=
.7 ½s. ^em mjmrfy kcs`rcmn ls ;73 ½A. D`r turj`j b`ssms, rmstrlgt tem nktk t` = ½s t` =.4 ½s. ^em mjmrfy kcs`rcmn cy tem O@WDM^ ls =7.7 ½A. Y`wmr ls ls nmtmroljmn nmtmroljmn ks ^
?
; d s
?
Ytur turj j ∓ `dd ?
; 39999 V ^ V
?
? = ½ s
;73 ½ A = ½ s =7.7 ½ A
? 34.> V .
Ytur turj j ∓ `j
?
^
?
? ;9.6 V .
= ½ s
D`r tem molttmr-d`bb`wmr nrlvm glrgult rmstrlgt tem nktk t` 3.= ½s t` 3.< ½s, flvljf 3;.7 ½A d`r turj-`dd. turj-`dd. Smstrlgt tem nktk t` = ½s t` =.7 ½s, flvljf ;3.5 ½A d`r d`r turj-`j. Y`wmr ls temj Ytur turj j ∓ `dd ?
V
?
V
Ytur turj j ∓ `j
?
3;.7 ½ A
?
;3.5 ½ A
^ ^
= ½ s = ½ s
? >.34 V .
? 3.=4 V .
c) D`r tem dlrst glrgult, pmkh fktm gurrmjt ls ;36 oK, kvmrkfm fktm gurrmjt ls zmr`, kjn ros fktm gurrmjt ls >5.= oK. D`r tem smg`jn glrgult, pmkh fktm gurrmjt gurrmjt ls >93 oK (kjn -576 oK), kvmrkfm fktm gurrmjt ls zmr`, kjn kj n ros fktm gurrmjt ls ;9< oK. ;9-3) D`r S ; ? 6= ά, t`dd ≅ ;.3 βs, t`j ≅ 9.4 βs, kjn YO@W ≅ 79 V. D`r S ; ? =9 ά, t`dd ≅ 9.55 βs, t`j ≅ 9.>3 βs, kjn YO@W ≅ 33 V. D`r S ; ? 3= ά, t`dd ≅ 9.=> βs, t`j ≅ 9.3> βs, kjn YO@W ≅ ;> V. Smnugljf nrlvm glrgult rmslstkjgm slfjldlgkjtby rmnugms tem swltgeljf tlom kjn p`wmr b`ss d`r tem O@WDM^.
;9-7) ^em vkbums `d Tl, S ;, S 3, kjn G oust cm smbmgtmn smbmgtmn d`r tem CA^ cksm cksm nrlvm glrgult. Dlrst, smbmgt Tl1 bmt Tl?39 T. T. temj, tem vkbum `d S ; ls nmtmroljmn dr`o tem ljltlkb gurrmjt splhm rmqulrmomjt. W`bvljf d`r S ; lj Mq. ;9-;, S;
?
Tl
∓ vCM L C;
?
39 ∓ ; =
? 7.5 ℤ
^em stmkny-stktm cksm gurrmjt lj tem `j stktm nmtmroljms S 3. Dr`o Mq. ;9-3,
S3
?
Tl
∓ vCM L C 3
39 ∓ ; ∓ S; ? ∓ 7.5 ? 7>.3 ℤ 9.=
^em vkbum `d G ls nmtmroljmn nmtmroljmn dr`o tem rmqulrmn tlo tlomm g`jstkjt. D`r k =9% nuty rktl` kt ;99 hEz, tem trkjslst`r ls `j d`r = ½s. Bmttljf tem `j tlom d`r tem trkjslst`r cm dlvm tlo tlomm g`jstkjts, ώ ? ;½s. Dr`o Mq. ;9-7,
G ? (7.>3)G ? ; ½ s ö S + S D ; 3 G ? 9.3) ^em vkbums `d Tl, S ;, S 3, kjn G oust cm smbmgtmn smbmgtmn d`r tem CA^ cksm cksm nrlvm glrgult. Dlrst, smbmgt Tl8 bmt Tl ? 39 T. T. temj, tem vkbum vkbu m `d S ; ls nmtmroljmn dr`o tem ljltlkb gurrmjt splhm rmqulrmomjt. W`bvljf d`r S ; lj Mq. ;9-;, S;
?
Tl
∓ vCM 39 ∓ ; ? ? 4.77 ℤ
L C;
7
^em stmkny-stktm cksm gurrmjt lj tem `j stktm nmtmroljms S 3. Dr`o Mq. ;9-3,
S3
?
Tl
∓ vCM L C 3
39 ∓ ; ∓ S; ? ∓ 4.77 ? 3=.7 ℤ 9.4
^em vkbum `d G ls nmtmroljmn nmtmroljmn dr`o tem rmqulrmn rmqulrmn tlom tlom g`jstkjt. g`jstkjt. D`r k =9% nuty rktl` kt ;39 hEz, tem trkjslst`r trkjslst`r ls `j d`r >.;6 ½s. Bmttljf Bmttljf tem `j tlom d`r tem trkjslst`r trkjslst`r cm dlvm tlom g`jstkjts, ώ ? ; ½s. Dr`o Mq. ;9-7,
S S ? S M G ? ; 3 ö G ? =.94 G ? 9.577 ½ s S; + S3 G ? 9.;4= ½ D
ώ
;9-=) k) Dr`o Mq. ;9-= ter`ufe ;9-6 ; 9-6 d`r t 2 t d , l[
t t 4 ? L B ; ∓ öö ? > ; ∓ ∓4ö ? > ∓ 5(;9) t t d 9.=(;9) L t
>t
4
lG ?
B
t d
?
9.=(;9) ∓4
L Bt 3
vG (t ) ?
?
3Gt d
? 5(;9)
t
>t 3
∓4
3(9.9=)(;9) (9.=)(;9)
∓4
? 5(;9);7 t 3
D`r td 2 t 2 t x,
lG
?9 ? L B ? >
vG
?
l[
L B G
(t ∓ t d ) +
L Bt d 3G
? 5(;9)6 (t ∓ 9.= (;9) ∓4 ) + 39
^lom tx ls nmdljmn ks wemj tem gkpkglt`r v`btkfm rmkgems Ts (=9 T.)1 vG (t x ) ? Ts
? =9 ?
5(;9)6 (t x
∓ 9.=(;9)4 ) + 39 ⇓
tx
? 9.56= ½ s
c) Vlte Vlte tx : td , tem wkvmd`ros krm blhm te`sm lj Dlf. ;9.;3(n). g) ^urj-`dd ^urj-`dd b`ss ls tem swltge swltge ls nmtmroljmn dr`o Mq. ;9-;3,
3 3
Y[
?
L B t d d 3>G
?
>3 X9 X9..=(;9)∓4 _3 (;39999) 3>(9.9=)(;9)∓4
? 9.> V .
Wjuccmr b`ss ls nmtmroljmn cy tem ko`ujt `d st`rmn mjmrfy lj tem gkpkglt`r tekt wlbb cm trkjsdmrrmn t` tem sjuccmr rmslst`r1
Y S
?
; 3
3 s
GT d
?
9.9=(;9) ∓4 (=9) 3 (;39999) 3
? 6.= V .
;9-4) Wwltge gurrmjt ls mxprmssmn ks
t t 4 ? L B ; ∓ öö ? > ; ∓ ∓4ö ? > ∓ 5(;9) t t 9.=(;9) d >t L Bt 4 lG ? ? ∓4 ? 5(;9) t l[
t d
vG (t ) ?
9.=(;9)
L Bt 3
3Gt d
?
>t 3 ∓4
3(9.9;)(;9) (9.=)(;9)
∓4
? >(;9);> t 3
Gkpkglt`r v`btkfm kt t ? t d ? 9.= ½s w`ubn cm ;99 v`bts, welge ls frmktmr tekj T s. ^emrmd`rm, tem kc`vm mquktl`js krm vkbln `jby ujtlb vG rmkgems Ts1
vG (t x ) ? Ts
? =9 ? >(;9);> t x3 ⇓
tx
? 9.7=> ½ s
D`r tx 2 t 2 td ,
? > ∓ 5(;9)4 t lG ? 9 vG ? T s ? =9 l[
c) Vlte Vlte tx 2 td , tem wkvmd`ros krm blhm te`sm `d Dlf. D lf. ;9.;3(c). Mquktl`j ;9-;3 ls j`t vkbln emrm cmgkusm tx 2 td . Wwltge p`wmr ls nmtmroljmn dr`o ^
Y[ ? ; ^
^
^
∨ p(t )nt ? ^ ; ∨ l v nt ? d ∨ l v nt ? [ [
9
9
[ G
9
t t 4 ;> 3 ;39999 ∨ > ∓ 5 ( ;9 ) t >(;9) t nt + ∨ > ∓ 5 ( ;94) t (=9) nt ? ;.5> V . t 9 d
x
x
Wjuccmr b`ss ls nmtmroljmn cy tem ko`ujt `d st`rmn mjmrfy lj tem gkpkglt`r tekt wlbb cm trkjsdmrrmn t` tem sjuccmr rmslst`r1
Y S
?
; 3
3 s
GT d
?
9.9;(;9∓4 (=9) 3 (;39999) 3
? ;.= V .
;9-6) G
?
S ? Y S Y[ ;9-5)
L Bt d 3T s
?
;9(9.;)(;9)∓4 3(;=9)
t `j N / d =G
? ?
; 3
?
=G
?
? 7.77 jD .
9.> / ;99999 (=) 7.77(;9)
∓<
? 3>9 ℤ
∓
(7.77(;9) < (;=9) 3;99999 ? 7.6= V .
L B3t 3d d ;9 3 X9.;(;9) ∓4 _3;9= 3>G
?
3>(7.77)(;9) ∓<
? ;.3= V .
G
?
S ? Y S Y[
L B t d
?
3T d
;9(9.;)(;9) ∓4 3(6=)
t `j N / d =G
? ?
;
?
=G
GTs3 d
?
?
;
? 4.46 jD .
9.> / ;9 ;99999 =(4.46)(;9)
∓<
(4.46) (4. 46)((;9 ;9))< (;=9) ;=9) 3;9 ;9999 9999 9 ? 6.= V .
3 3 3 L B t d d ;93 X.;( X.;(;9)∓4 _3;9=
?
3>G
? ;39 ℤ
3>(4.46)(;9)
∓6
? 9.43= V .
;9- / ;3=999
?
d
? 43.3 ℤ
=(;9.7)(;9) ∓<
;
3 s
? ;9.7 jD .
∓<
? 3 (;9.7)(;9)
3
(;69) ;3=999 ? ;5.4 V .
L B3t 3d d ;93 X9.=(;9) ∓4 _3;3=999 3>G
?
3>(;9.7)(;9) ∓<
? 4.3 V .
;9-;9) G
?
S ? Y S Y[
L B t d 3T d
?
6(9.=)(;9) 3(;3=)
t `j N / d =G
? ?
; 3
?
=G
GTs3 d
?
?
; 3
∓4
? ;>.9 jD .
9.> / ;3 ;3=999 =(;>)(;9) ∓<
? >=.6 ℤ
(;> ;>)( )(;9 ;9))∓< (;6 ;69) 9)3;3 ;3=9 =999 99 ? 3= 3=.7 .7 V .
L t d ;93 X9.=( X9.=(;9)∓4 _3;3=999 ;3=999 3 3 B d
3>G
?
3>(;>)(;9) ∓<
? >.=4 V .
;9-;;) ]sljf tem sjuccmr glrgult `d Dlf. ;9-;3(k), Mq. ;9-;3 ylmbns G
?
L B3t 3d d =3 X9.=( X9.=(;9) ;9)∓4 _3 399999 399999
?
? =3.; jD .
3> Y [ S ? Y S
3>(;)
t `j N / d =G
?
; 3
?
=G
GTs3 d
?
?
; 3
9.7= / 399999 =(=3.;)(;9)
∓<
? 4.63 ℤ
(= (=3. 3.; ;)( )(;9 ;9)) ∓< (5 (59) 9)3 39 3999 9999 99 ? 77.7 77.7 V .
;9-;3) ]sljf tem sjuccmr glrgult `d Dlf. ;9-;3(k), Mq. ;9-;3 ylmbns G
?
S ? Y S
L B3t 3d d 43 X; X;(;9)∓4 _3 ;99999 ;99999 3> Y [
?
3>(3)
t `j N / d =G
?
; 3
?
=G
GTs3 d
?
?
; 3
9.7 / ;9 ;99999 =(6=)(;9) ∓<
? 6= jD .
? 5.9 ℤ
(6 (6= =)( )(;9 ;9))∓< (;3 ;39) 9)3;9 ;999 9999 99 ? => V .
;9-;7) k) Dr`o r`o Mq. (; (;99-;4 ;4), ), ^ A
c) Y ?
^ A
? ^K + Y ( Sε , AK ) ? 79 ¹ + 3 ( >9) ? ;;9 ;;9¹ G
∓ ^ K ;=9 ∓ 79 ? ? 7 V
Sε , AK
>9
;9-;>) k ) Dr`o Mq. (;9-;4), ^ A
c) Y ?
^ A
? ^K + Y ( Sε , AK ) ? 3=¹ + ;.= ( == ) ? ;96.=¹ G
∓ ^ K ;6= ∓ 3= ? ? 3.67 V
Sε , AK
==
;9-;=) ^ A
? Y ( S , AG + S ,GW + S , WK ) + ^K ? ;9 ( ;.; + 9.< + 3. 3.= ) + >9 ? 5 =¹ G
^ A
7.9 ) + 3= ? = 7. 7.=¹ G ? Y ( Sε , AG + Sε ,GW + Sε ,WK ) + ^K ? = ( ;.= + ;.3 + 7.
^ A
? Y ( Sε , AG + Sε ,GW + Sε ,WK ) + ^K
ε
ε
ε
;9-;4)
;9-;6)
Sε , WK
?
^ A
∓ ^ K Y
;;9 ∓ >9 ;.9 ? 3.;< ¹G / V ∓ Sε , AG ∓ Sε ,GW ? ∓ 9.6 ∓ ;. ;5
;9-;5) Dr`o Dlf. ;9.3> usljf tem c`tt`o gurvm d`r k sljfbm pubsm, Qε , AG ≅ 9.9;7 ¹G / V d`r k pubsm `d ;9 ∓= smg.
∄^ A ? Yno Qε , AG ? ( =99V ) ( 9.9;7 ¹G / V ) ? 4.=¹ G
;9-;, Qε , AG ≅ 9.;; ¹G / V .
∄^ A ? Yno Qε , AG ? ( ;99 ) ( 9.;;) ? ;;¹ G c) ]sljf S ε , AG ? ;.9= ¹G / V ,
∄^ A ? Ykvf Sε , AG ? ( Yno N ) Sε , AG ? ;99 ( 9.;) ;.9= ? ;9.=¹ G.
J`tm tekt tem vkbum `d Q d r`o tem frkpe ls vmry r`ufe, kjn o`rm prmglsm prmglsm mvkbukt mvkbuktl`j l`j lj (k) ls gb`smr gb`smr t` tem ;9.=¹ `d pkrt (c).
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