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Mrnsfayenctajadk Mrnsfayenc ta taja jadk dk ;0 ;0-8 ;0-8;-8; ;-88 -8 88;0 8; ;0 0

K Kckensnsda ckensnsdasnstafks snstafksda dapgtacmnk pgtacmnk; ;

?.;.Fgdn`nquaaeprgbrkfkacaeAjafpeg?.;pkrkquaaeusukrngpuadk ncbraskrekssnbunactasmkctndkdas:KfpentudfëxnfkdaedadgdaepnaPf, ncbraskrekssnbunactasmkctndkdas:Kfpentudfëxnfkdaedadgdae pnaPf, yaeëcbuegda`ksaGvdaesufncnstrgsncusgndkev(t)6Pfmgs(wt+Gv) fkbcntuddanfpadkcmnkdaedadgdaepnaZ,yaeëcbuegda`ksa.^gdaek mkrbk.Aeprgbrkfkdaoaprgdumnrbrë`nmgspkrkn(t),v(t),p(t),Xr(t)yXx (t),snf-Mgfgacaeajafpeg AjamutaaeprgbrkfkpkrkPf6;88P,Gv6Gyekssnbunactasmkrbks: Qckmkrbk Qck Qckmkrbkncdumtnvk,Z6;.?10 mkrbkncdumt ncdumtnvk, nvk,Z6 Z6;.?10 ;.?10 508◠℠ Qckmkrbkmkpkmntnvk,Z6?.805 Qckmkrbkmkpkmntnvk,Z6?.80 5∟=8◠℠ Qckmkrbkrasnstnvk,Z6?.10 Qckmkrbkrasnstnvk,Z6 ?.105 58◠℠

(k)Daeksbrë`nmksXr(t)yXx(t),astnfaekpgtacmnkrakeyrakmtnvkpkrk mkdkmkrbk.]kquauckmgcmeusnýcsgoraaesnbcgdapgtacmnkrakmtnvk pkrkncdumtnvgymkrb pkrkncdu mtnvgy mtnvg y mkrb mkrbks ks mkpkmntnvks mkpkmntnvks. mkpkmntnvks. (o)Qtn (o (o) )Qtnen Qtnenz Qtnenzkcdg enzk zkcd kcdgvkeg cdgvke gvkeg vkegras gras `ksgrn `ksgrnkeas `ksgrnkeasda keasda keasda mgrrnactayvgetkja,mkemueaekpgtacmnkrakeyrakmtnvkpkrkmkdkmkrbky mgfpëraekmgcegsrasuetkdgsgotacndgsdaeksmurvks.(a)]ntgdkseks mkrb mk rbks ks k kcta ctarn rngr  gras as a astë stëc c m mgca gcamt mtkd kdks k s  k  ttrkv rkvîs   îs îs da da ek ek ek f fnsf nsfk k  `uac `uacta ta d da a kenfac ken factkm tkmnýc nýc, , d datar  atarfnc fnca a eek ek k pg pgttacmnk pgtacm nk nk rak ra rake ke y y rak ra rakmtn kmtnvk vk tg vk tgt tgtke tke ke tg tgf tgfkdk fkd kdk k da da ek `uacta.

k k)) E Ekpgtacm kpgtacmnkk nkkmtnvk mtnvk,rak ,rakmtnvk mtnvkykp ykpkracta kracta ;)   Z;6;.?1 5 08 ¸ ℠ ,

 

?) Z?6 ?.80 5∟=8 ¸ ℠     =) Z= 6?.10 5 8 ¸ ℠

]6 ?888 + J=40= ]6 ?;01∟ J;?4> ]6 ?888 + J8 8

o) o) P Pf f6; f 6;8 8 88 8 Z;

N6

ℛ 5 8 ¸ P 28.2;? 5 8 ¸ 6 6  610.10> ↘ 08 ¸K √? Z ;.?1 5 08 ¸

X6P−Nmgs Nmgsιι 628.2;?P*10.10>K*mgs08¸ X6?888 R [6P−Nsac Nsacιι 628.2;?P*10.10>K*mgs08¸ [ 6=404 P  P K_ K_

 

 

Z?

P 28.2;? 5 8 ¸ N6 6  6=1.=0 5 =8 ¸K Z ?.8 ↘ =8 ¸ X6P−Nmgs Nmgsιι 628.2;?P*=1.=0K*mgs-=8¸ X6?;01 R 28.2;?

=1.=0

mgs

P* K* [ 6P−Nsac Nsacιι 6 [6∟ ;?18 P  P K_ K_

-=8¸

Z=

P 28.2;? 5 8 ¸ N6 6    6?9.?> 5 8 ¸K Z ?.1 5 8 ¸ X6P−Nmgs Nmgsιι 628.2;?P*?9.?>K*mgs8¸ X6?888 R [6P−Nsac Nsacιι 628.2;?P*?9.?>K*mgs8¸ [6 8 P  P K_ K_ ;

?

=

?888

?888

?;01

XT6X +X +X 6 R+ X6 0;01 R

R+

R

[T6 [ ; + [ ? + [ = 6=404 P  P K_ K_ ∟;?18 P P  K_ K_ + 8 P P  K_ K_ [T6 ??;4 P  P K_ K_

?.?.]asufncnstrkuckmkrbkfgcg`ësnmkmgcucvgetkjasncusgndkev(t)6 ?88mgs(=22t)Ekpgtacmnkncstkctëcakrasuetkctaasp(t)6988+;888mgs (214t-=0.92º)(k)Acmuactraekpgtacmnkmgfpeajksufncnstrkdkkekmkrbk. (o)Acmuactraekmgrrnac (o)Acmuac traekmgrrnactancstkct tancstkctëcakn(t)yaevkegra`nmkzdaekmgrrnac ëcakn(t)yaevkegra`nmkzdaekmgrrnacta ta sufncnstrk sufnc nstrkdkkek dk kek mk dk mkrb mkrbk. rbk. k. (a (a)A (a)Acmuactraeknfpad )Acm cmua uactraeknfpadkcmn kcmnkdamkrbk.(d)Qsa kdamkrbk.(d)Qsa FKTN.KOpkrktrk FKTN.K Opkrktrkzkrv(t), zkrv(t),p(t)an(t)6p(t) p(t)an(t)6p(t)/v(t)rkcbg /v(t)rkcbgsuparng suparngrdaGk rdaGk ;0.02fsacpksgsda8.;fs.Kpkrtnrdaekbrë`nmkkmtuke,astnfaek kfpentudfëxnfk,aeëcbuegda`ksayek`ramuacmnk kfpentudfëxnfk,ae kfpentudfëxnfk,aeëcbuegda ëcbuegda`ksayek`ramuacmnkkcbuekrdaek `ksayek`ramuacmnkkcbuekrdaekmgrrnacta, kcbuekrdaekmgrrnacta, yvarn`nquaegsrasuetkd yvarn`nqu aegsrasuetkdgsgotacnd gsgotacndgsacekpkrta(o).Tacbkacmuact gsacekpkrta(o).Tacbkacmuactkac kac FKTNKOaemgfkcdgpkrkkrrkygek FKTNKOaemgfkcdg pkrkkrrkygekdnvnsnýcaeafactgpgr dnvnsnýcaeafactgpgraeafactgas. aeafactgas.

X ( t)6 N Nmg mgss ι ( ; + mgs? ( wt+ ιv )) Nsacιι ( ; + sac ? ( wt+ ιv )) )6 P−Nmgs ))+ + P−Nsac X ( t)6( )6(988−;888 )( mgs ( 214 t) mgs ( =0.92 º)+ sac ( 214 t) sac ( =0.92 º)) X ( t)6 )6 988 + 988mgs ( 214 t))+ + 088 sac ( 214 t) X ( t)6 )6 988 ( ; + mgs ( 214 t))) ))+ ) + 088 sac ( 214 t) X6 ·988R

[6088PK_

]·988+ J088

 

 

Tkcbι 6

  [   088 6 X 988

ι 6=0.92º P6

Pf 5 8 ¸

√?

6

?88 ¸

√?

6;4;.4?5 8 ¸

X6PÒNmgsι N6

    X X    988 6 62.82K Pmgsι ;4;.4?

ℛ6√? ÒN6√? Ò 2.82K 6;8K

?.= Qck ?.= Qck mkr mkrbkncdum bkncdumtnv tnvkmgcsns kmgcsnstaac taac _y Yac sar sarnakenfa nakenfactk ctkdgdasda dgdasda ?488P ?488 P Prrfs fs fs s supenacd upenacd nacdg g kosgro kosgronacd nacdg?99lRacuc`kmtg nacd g?99lRacuc`kmtgrdapgtacm rdapgtacmnkac nkac ktrksgda8.9.Datarfnck_yY.

ι 6mgs∟; 8.9 6 =0.92 ¸ ]6

?99 8.9

 LPK LP  K K 5 =0.92 6=08 5 =0.92 ¸ LP ]6 PN

N6

=

↘ =0.92 ¸    6;18 ↘ =0.92 K ?488 5 8 ¸

−

=08 ;8

P    ?488 5 8 ¸ Z6_ + JY6  6 6;?.9 + J>.0 ή ;18

N

=0.92

¸ ↘ _ 6;?.9 ή Y6>.0 ή

?.4Qckmkrbkncdumtnvkmgcsnstaac_yYacpkrkeaegkenfactkcdgk ?488Prfssupenacdgkosgronacdg?99lRacuc`kmtgrdapgtacmnkac kdaekctgda8.9.Datarfnck_yY.

]6

?99 8.9

5 =0.92 ¸6=08 5 =0.92 ¸

]6 ?99LR+ J?;0LP  LPkr kr

 

 

|P | ?

_ 6

X

6

   ?488

−

? =

?99 ;8

6?8 ή

P?    ?488 ? Y6 6 6?0.002 ή [ ?;0−;8=

?.1.Dgsmkrbksacpkrkeaegsamgcamtkckuck`uactafgcg`ësnmkda ?48Prfs.Eksdgsmkrbksmgcsufacuckpgtacmnkraketgtkeda488lRmgc uc`kmtgrdapgtacmnkda8.9acktrksg.Qckdaeksmkrbksmgcsufa;?8lR mgcuc`kmtgrdapgtacmnkda8.>0ackdaekctg.Acmuactraekpgtacmnk mgfpeajkdaekgtrkmkrbk.

X?6XT∟X;6 488 lR∟;?8 lR6 ?98 lR     X X    488 lR NT6 6 6 ?89=.==K Pmgs ( ι ) ?48 P−8.9     X X;    ;?8 lR N;6 61?8.9==K 6 Pmgs ( ι ) ?48 P−8.9 ?89=.==

N?6NTT∟N;6

1?8.9==

K ∟

;10?.1

K 6

K

P  K_ K_ [?6PNsnc ( ι )6PNsnc ( mgs∟; `p )6?48 P−;10?.1 K −snc ( mgs∟; 8.>0 )6;81888 P

´]6 ?98 +j´ ;81lPK· ?>>.84 lP  lP lPK  K K ∗ ?8.110 º ?.0. ?.0. 0. Ek Ek mk mkrb rbk k f fgst gstrk rkdk dk ac dk ac ek ek `n `nbu burk rk rk mg mgcs cstk tk tk da da uc uck k _ _asn asnst stac acmn mnk k _ a ac c pkrkeaegmgcucmkpkmntgrdarakmtkcmnkY.Ekmkrbkaskenfactkdkpgruck `uactafgcg `ua ctafgcg`ës `ësnmkk nm nmkk kk tr trk trkvîsda kvî vîsda sda uc uck k eæ eæc eæcak cak ak da danfpadkcm da nf nfpa pad dkcmnk nk   9.4 +j ;;.?℠.Ae vgetkjarfsacegstarfnckeasdaekmkrbkas;?88∗8ºPrfsyekmkrbk mgcsufa=8lPKmgcuc`kmtgrda mgcsufa=8lPKmgc mgcsufa=8lPKmgcuc`kmtgrdapgtacmnkda8.9ackdaekctg. uc`kmtgrdapgtacmnkda8.9 pgtacmnkda8.9ac ac kdaekctg.

 (k)Acmuactraaevkegrda_yY.

?

ι6

mgs∟; 8.9

?

?

_ 6  PN  P ι 6 ] P`p X 6PNmgs ι 6 P 6∟=0.92 º º 8 º6;?18 ∗ ;0.?0 ºº P P´ T6P

?.2Dgsnfpadkcmnks,Z;6 ?.2Dgsnfpadkcm nks,Z;68.9+J1.0℠yZ? 8.9+J1.0℠yZ?69”j;0℠yucfgtg 69”j;0℠yucfgtgr r fgcg`ësnmgastëc fgcg`ë snmgastëcmgcamtkdg mgcamtkdgsacpkrkeaegkuck`uacta sacpkrkeaegkuck`uactada?88Prfs da?88Prfs k08Iz,mgfgsafuastrkaceknfkba k08Iz,mgfgsafuas trkaceknfkbac.Aefgtgrtna c.Aefgtgrtnacauckpgtac cauckpgtacmnk mnk da1lPKmgcuc`kmtgrdapgtacmnkda8.9daktrksg(ekmgrrnactasa ktrkskkevgetkja) k)Acmuactrkekspgtacmnksmgfpeajkspkrkeksnfpadkcmnksypkrkae fgtgr:

··· ];6  ·· P ∩ Z 6 ?

;

?

]?6  ·· P ∩

 · ·

 

?

?88

8.9

∟ J1.0

  ?88

6 6;888+  ;888+j2888  j2888PK PK

?

6;888” ;8 ;888”j?888  j?888PK PK Z? 6 9 + J;0  6 ·

]=6   1888 5 =0.92 ¸ 64888+J=888PK

Xgregtkctg,ekpgtacmnkmgfpeajkas: ]t60+j96   ;8 5 1=.;= ¸lPK

   

o)Datarfncaekpgtacmnktgtketgfkdkpgrek`uacta,ekmgrrnactayae `kmtgrdapgtacmnk.

N6

↘ 1=.;= ¸ 618ˏ-1=.;=K ?88 5 8 ¸

  ;8888

@X6mgs1=.;=68.0mgrrnacta ratrkskdkkevgetkja.

m m))  Q Qc c m mk k kp p pk k km mn mnntttg g grr  a as s stttë ë mgca mg camt mtkd kdg g ac p pkrk krkea eaeg eg m mgc gc  eeks ks  m mkrb krbks ks. . A Acmu cmuac actr  tra a ek p pgta gtacm cmnk nk rakmtnvkyekmkpkmntkcmnkac±@pkrkkmarmkrae`kmtgrdapgtacmnkk ;.·Muëeasekcuavkmgrrnactadaeæcak7

· Zm6  ·· P ∩ ··6 ?

]m

 

?

  ?88

J9888

 6-j1℠ 6-j1℠

0

;8

M6 ( ? ψ)( 08 )( 1 ) 61=8.1±@

N6

58 ¸  ̊ K 6=8ˏ8 ?88 5 8 ¸

  0888

?.9 Dgs ?.9 Dgs `ua `uacta ctas s fgc fgcg`ë g`ësnm snmks ksda davge vgetkj tkja a nda ndakea keas s ast astëc ëcmgc mgcamt amtkdk kdks s pgruckeæcakdanfpadkcmnkda8.2+j?.4℠mgfgsafuastrkacek  ̊ P.Acmuactraekpgtacmnk `nburk.P;6188ˏ;0.?0 ̊ PyP?6191ˏ8 mgfp mg fpea eajk  jk  pk pkrk rk m mkdk kd k  f fëqu ëqunc nck k y d data atarf rfnc nca a sn a ast stë stë ëc c c d dkcd kcdg g g ramnonacdgpgtacmnkrakeyrakmtnvk.Tkfonîc,acmuactraekpîrdndk dapgtacmnkrakeyrakmtnvkacekeæcak.

N6

  188

5 ;0.?0 ¸ ∟191 5 8 ¸  ̊ K 64?+j10628ˏ1=.;= 8.2 + j ?.4

 ̊ P)(28ˏ1=.;=  ̊ K)6=1888ˏ-=0.92  ̊ 6?9888-j?;888 ];?6   P;N·;?6(28ˏ;0.?0 PK  ̊ P)(-28ˏ-1=.;=  ̊ K)648>18ˏ-1=.;=  ̊ 6-?4128+j=?208 ]?;6   P?N·?;6(191ˏ8 PK

   

MgfgX;aspgsntnvgyX?ascabktnvg,ek`uac MgfgX;aspgsntnvgyX?ascabkt nvg,ek`uacta;bacark?9Lw, ta;bacark?9Lw,yek? yek? ramnoa?4.12lR,yekpîrdndkdapgtacmnkrakeas=.4=lR. ramnoa?4.12lR,yek pîrdndkdapgtacmnkrakeas=.4=lR. Mgfg[;ascabktnvg,ek`uacta;ramnva Mgfg[;ascabktnvg,ek`ua cta;ramnva?;lvkryek`uacta?actr ?;lvkryek`uacta?actrabk abk =?.20lvkr.Epîrdndkdapgtacmnkrakmtnvkas;;.20lvkr. =?.20lvkr.Epîrdndkdapgtacmnkrakmtnvk as;;.20lvkr.

?.>)AsmrnokucprgbrkfkFKTEKOpkrkaesnstafkdaeajafpeg ?.1dafgdgquaaevgetkjaekfkbcntuddaek`uacta;mkfonk dae21pgrmnactgke;88pgrmnactgdaevkegrdkdgacpksgsda; vget.Ekfkbcntuddaevgetkjadaek`uacta?yegsëcbuegsda `ksadadgs`uactasdaoacfkctacarsamgcstkctas.Mkemueaek pgta pg tacm cmnk nk m mgfp gfpea eajk  jk pk  jk pkrk rk m mkdk kd k ``uac uacta ta y Ek p pîrd îrdndk ndk nd k d da da a eæca eæ cak. k. Tkoueaekspgtacmnksrakmtnvksytrkma[ ;, [? y [E `r `rac acta ta ke vgetkjafkbcntud ||P |.Kpkrtnrdaegsrasuetkdgs,dafuastraqua ae`eujgdapgtacmnkrakmtnvkkegekrbgdaeeknctarmgcaxnýcastë datar  da tarfn fnck ckdk d k pgr p gr ek dn`a d n`ara racm cmnk nk da f fkbc kbcnt ntud u d  d a egs egs v vget getkj kjas as tarfnckeas. ;

A;6ncput(']gurma#;PgetkbaFkb.6')< k;6ncput(']gurma#;XiksaKcbea6')< A?6ncput(']gurma#?PgetkbaFkb.6')< k?6ncput(']gurma#?XiksaKcbea6')< _6ncput('Enca_asnstkcma6')< Y6ncput('Enca_akmtkcma6')< Z6_+j*Y