OEII Resenja Zadataka

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    1. 1 : 201 LXR , 101LX

    A4

    cos22)(1

    tti .

    a) 2R 2CX 2R

    )(1 ti , 2/ .

    ) )(t .

    1 1.1

    ______________________________________________________________________________

    Aj)1(2e22 4/j

    1

    I .

    ) , A22m2 I rad424

    2

    I ,

    2R Aj)1(2e22 4/j

    2

    I .

    1.1 1R 1LX

    2R 1CX :

    222111 )j()j( IXRIXR CL .

    102R 202CX .) :

    Vj)1(60)j()(j)j(j 111211113 IXRIIXIXRIXE LLLL ,

    V)4/cos(260)( tte .

    2. 2 : Vcos66)( ttu , ,11 R 21LX

    .32 LX ,R )(1 ti )(tu

    2 , A261I

    2R

    +

    1R

    C2X

    L1X

    LX

    1

    2

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    2 2.1

    ___________________________________________________________________________________

    2

    cos12)(1 tti .

    )(1 ti (u

    A12j1I V66U .

    2.1 :

    Vj212j 1111 IXRU ;

    A14j4j 2

    12

    LX

    UUI ;

    Aj2212 IIIR .

    R

    61

    RI

    UR .

    3. 3 : Vsin2)( tte , A)4/cos(22)(1 ttj ,

    Aj)3(2 J , rad/s105 , H10L F5C .

    .

    3 3.1

    ______________________________________________________________________________

    .

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    V)2/cos(2sin2)( ttte , V2je2 2/j E ,

    A)4/cos(22)(1 ttj , Aj)1(2e22 4/j

    1

    J .

    1LXL 2/1 CXC , .

    .

    3.1, :

    1210jj

    1

    j

    1JJ

    X

    EU

    XX LCL

    .

    Vj)3(210 U .

    ,

    A6jj

    10

    L

    EX

    UEI , VA6

    2

    1 * EE IES .

    : Vj)3(21021 UUU JJ .

    : VA)2j1(42

    1 *111 JUS JJ VA10

    2

    1 *222 JUS JJ .

    4. 4 : A4cos2)( tti ,

    V)2/cos(20)( tte , rad/s104 , mH2,10 LR F5C . .

    4 4.1

    ______________________________________________________________________________

    Aj)1(e2 4/j J V20je20 2/j E ,

    20LXL 20/1 CXC , .

    .

    , :

    JR

    EU

    XR C

    10

    j

    11.

    Vj)1(2010 U .

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    4/3j10 e2Aj)1(j

    C

    CX

    UI ,

    A)4/3cos(2)( ttiC .

    R ,

    A2 JII CR .

    : VA202

    1 2 RR IRS , VA20jj

    2

    1 2 JXS LL

    VA20j)j(2

    1 2 CCC IXS , :

    VA20j2

    1 *1 RE IES VAj)1(20

    2

    1 * JUS JJ ,

    V40jj 10 UJXU LJ .

    , VA20gp

    SS .

    5. 5 o je: V,41E V,3j2E

    A,j1J 121 LL XXR 2CX . .

    5 5.1______________________________________________________________________________

    5.1, ,

    21jjj

    1

    j

    1

    j

    1 2110

    2 LCCLL X

    E

    X

    EJU

    XXRX

    .

    V2j10U .

    :

    A1j

    2

    1022

    LX

    UEI , Aj1

    j1

    103

    LXR

    UI A2j1231 IJII .

    :

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    A2arctancos51 ti , Acos2 ti A4

    cos23

    ti .

    : Vj110 JRUUJ ,

    a :

    VAj2

    1 * JUS J , VA2j122

    1 *111 IS

    VA

    2

    3j

    2

    1 *222 IS .

    6. 6 o je: V,5j1E V,20j52 E

    V,10j103 E V,10j4 E 12LC XXR 21LX . .

    6 6.1

    ______________________________________________________________________________

    .

    6.1, :

    V10j10320 EU ;

    V10j430 EU ;

    2

    213020

    1

    10

    21 jjj

    1

    j

    1

    j

    1

    j

    1

    j

    1

    LCCLCLL X

    E

    X

    EU

    XU

    XU

    XXX

    .

    V20j10

    U .

    :

    A5jj

    103013111

    CC X

    UUE

    X

    UEI , Aj15

    jj1

    2010

    1

    126

    LL X

    UU

    X

    UI , A5j162 III ,

    A103020235

    R

    UU

    R

    UI , A5154 III Aj15243 III .

    :

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    VA502

    1 25 IRSR , VA50jj

    2

    1 2611

    IXS LL , VA2

    25jj

    2

    1 2222

    IXS LL

    .VA2

    25j)j(

    2

    1 21 IXS CC

    :

    VA225j

    21 *

    111 IESE , VA)225j50(

    21 *

    222 IESE , VA50j21 *

    333 IESE

    VA25j2

    1 *444

    IESE .

    , VAj)1(50gp SS .

    7. 7

    . : ,)j1(,j,)j1( 321 ZZZ

    V)2j6(1 E A2j2J .

    7 7.1

    ______________________________________________________________________________

    .

    . , , 7.1.

    , 2II JI ,

    I

    1II3I31 )( EIZIZZ .

    I A231

    231I

    ZZ

    JZEI .

    7.1,

    :

    A2I1 II A22Aj)1(2 4j

    2I2

    eJII .

    :

    Acos21 ti , A4

    cos222

    ti A2

    cos22

    tj .

    1Z_

    2Z_

    E_

    +

    J_13Z_

    2

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    8. 8 .

    : ,2,j)1(,)2j2( 321 ZZZ 2j4Z , ,1 V10, 12 E V8j2E .

    88.1______________________________________________________________________________

    .

    8.1, : Aj1I JI Aj2II JI , :

    12II43I31III4321 )()()( EEIZZIZZIZZZZ .

    A2jIII I .

    8.1, :

    AjIIII1 III , A2jIII2 II , A2jIIIIII3 IIII A3jIIIII4 III .

    :

    VAj)1(2

    1 2111 IZSZ , VAj)1(2

    2

    1 2222 IZSZ , VA4

    2

    1 2333 IZSZ

    VA9j2

    1 2444 IZSZ .

    :

    VA5j2

    1 *111 IESE VA8

    2

    1 *222 IESE .

    :

    V)6j8(222441 IZEIZUJ V)4j6(33442 IZIZUJ ,

    : VA)4j3(2

    1 *111 JUS JJ VA)3j2(

    2

    1 *222 JUS JJ .

    , VA)12j7(gp

    SS .

    +

    1E_

    3Z_ 4Z_

    1J_

    2Z_1Z_

    +

    2E_

    2J_

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    9. 9 : ,21 R ,132 RR ,221 LL XX ,13 LX ,1CX V,j21 E V,2j12 E A11 A2 .

    e e .

    9 9.1

    ______________________________________________________________________________

    9.1 :

    A11JII ;

    Aj2II JI ;

    21II33I233III23311 jjjjjj EEIXRIRXXRIRXXRXR LCLCLL ,

    III

    Aj

    jjj

    jjj

    23311

    233123321

    III

    RXXRXR

    JXRJRXXREEI

    CLL

    LCL .

    9.1 :

    AjIII1 II , Aj1III2 III I , A1223 JII A0124 IJI .

    :

    VA2j12

    1

    2

    1 *111 IS

    VA0

    2

    1 *222 IS .

    :

    Vj3jj 223331 IXRIXRU CLJ

    Vj4jj 2333222 EIXRJXU LLJ ,

    :

    VAj32

    1

    2

    1 *111 JUS J VA4j1

    2

    1

    2

    1 *222 JUS J .

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    10. 10 .

    : 10431 LC XXRRR , 52R , Vcos100)(1 tte ,

    V2

    cos100)(2

    tte )62( .

    10 10.1______________________________________________________________________________

    .

    Vcos100)(1 tte , V100e100 0j

    1 E ,

    V)2/cos(100)(2 tte , V100je100 2/j

    2

    E .

    .

    10.1,

    A)3j1(2III JI ,

    :

    1II3I31 j)j( EJXIRIXRR CC ;

    2II43I3 j)j( EJXIXRRIR LL .

    : Aj)3(I I A)7j1(II I .

    10.1, :

    Aj)3(I1 II , Aj)1(5IIII2 III , A)3j1(2III3 III ,

    A)7j1(II4 II Aj)3(IIIII5 III .

    :

    VA502

    1 2111 IRSR , VA100

    2

    1 222 JRSR , VA200

    2

    1 2333 IRSR ,

    VA2502

    1 2444 IRSR , VA50jj

    2

    1 25 IXS LL VA250j)j(

    2

    1 22 IXS CC .

    :

    2

    +

    E3R

    J

    1

    4R 2

    R

    E

    1

    CX

    LX

    +

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    VAj)3(502

    1 *111 IESE , VAj)7(50

    2

    1 *422 IESE VA)2j1(100

    2

    1 * JUS JJ ,

    Vj)7(10jj 225 JRIXIXU CLJ .

    , VAj)3(200gp SS .

    11. 11 : ,j1,j 521 ZZZ ,13 Z

    ,j4 Z V,j)1(V,1 21 EE A21J Aj12 J .

    .

    11 11.1

    ______________________________________________________________________________

    :

    Aj12III JI ;

    A21VI JI ;

    2III3II3I43 EIZIZIZZ ;

    21VI1III3II531I3 EEIZIZIZZZIZ .

    :

    A1II A1II I .

    :

    A1I4 II , A1IIIV1 III , A1II5 II , A0IIIIIE III

    A1IIIIII3 IIII .

    :

    Vj1111 IZUJ Vj31155222 IZIZJZUJ .

    : VAj1

    2

    1 *111

    JUS JJ , VA2j12

    1 *222

    JUS JJ , VA02

    1 *11 EE IES

    VAj12

    1

    2

    1 *322 IESE .

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    12. 12 .

    : j)1(21Z , )2j1(22Z , j)1(3Z , j)1(4Z , 55Z ,

    V)j2(1 E , V)2j1(2 E , Aj1 J A12 J .

    12 12.1

    ______________________________________________________________________________

    .

    12.1, :

    Aj1I JI

    A12II JI ,

    21II43I42III4321 )()()( EEIZZIZZIZZZZ .

    AjIII I . 12.1, :

    AjIII1 II , A0IIII2 III , Aj)1(IIIII3 III A1134 JII .

    :

    VAj)1(2

    1 2111 IZSZ , VA0

    2

    1 2222 IZSZ , VAj)1(

    2

    1 2333 IZSZ ,

    VAj)1(2

    1

    2

    1 2444 IZSZ VA

    2

    5

    2

    1 2555 IZSZ .

    :

    VA)2j1(21

    21 *

    111 IESE VA0

    21 *

    222 IESE .

    :

    Vj)2(442221 IZIZEUJ Vj)8(2533442 JZIZIZUJ ,

    :

    +

    +

    1E_

    2E_

    Z_Z_

    1Z_

    4Z_

    2Z_

    3

    5Z_

    1J_

    J_2J_

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    VA)2j1(2

    1

    2

    1 *111 JUS JJ VAj)8(

    2

    1

    2

    1 *222 JUS JJ .

    , VA)5.0j5(gp SS .

    13. 13 e e 3R . : ,131 RR ,1CX

    ,242 RR ,4LX V,jE jA1J A43

    cos22

    tj .

    13 13.1

    ______________________________________________________________________________

    .Aj12 J :

    1I JI ;

    2II JI ;

    EIRIXIXRXR CCL II4IIII41 jjj ,

    Ajjj

    j

    41

    241III

    CL

    C

    XXRR

    JRJXEI .

    , 13.1, :

    A52j1 )2arctanj(213 eJJI , AjIII1 II , A2jIII12 IJI

    A1IIIII4 III .

    :

    V4j1j123321

    JRIRIXUCJ

    V2j333442

    IRIRUJ

    .

    :

    VAj42

    1

    2

    1 *1

    11 JUS JJ , VAj5

    2

    1

    2

    1 *222

    JUS JJ VA2

    1

    2

    1 *1 IESE .

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    14. 14

    e e . : ,221 RR ,13 R ,31 CX ,12 CX ,2LX V,2cos9)( tte A2cos3)(1 ttj Acos6)(2 ttj .

    14 14.1______________________________________________________________________________

    , : V9je9 2

    j

    E ; A3je3 2j

    1

    J ; A6e6 0j2 J .

    14.1 :

    A3j1I JI ;

    A62II JI ;

    EIXRIRIXRR CC II11I3III131 jj ,

    A4j

    j

    131

    21113III

    C

    C

    XRR

    JXRJREI .

    :

    A3j6212 JJI , A2IIIII1 III , A3j4123 III A4III4 II .

    :

    V3j7j 1233221 JRIRIXU CJ V7j 21212 JXEJRUU LJJ .

    :

    VA18j2

    1 *4 IESE , VA7j3

    2

    3

    2

    1 *111

    JUS JJ VA212

    1 *222 JUS JJ .

    15. 15 o je: V,5j51 E V,105E V,25j6E A,3j11 J A,j32 J ,51 Z ,10j2 Z ,j133 Z 5j5Z .106 Z .

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    15

    ______________________________________________________________________________

    15.1 :

    A3j11I JI ;

    Aj32II JI ;

    56III65II5 EEIZZIZ .

    15.1

    , III

    Ajj)2(5

    515j1025j

    65

    2556III

    ZZ

    JZEEI .

    :

    AjIII6 II , A23625 IJI , A3II3 II A2j4212 JJI .

    :

    V50j20221111 IZEJZUJ V13j1422335552 IZIZIZEUJ .

    :

    VA55j652

    1 *111

    JUS JJ , VA25j552

    1

    2

    1 *222

    JUS JJ ,

    VA,5j102

    1 *111

    JESE VA10j152

    1 *555

    IESE , VA2

    25

    2

    1 *666 IESE ,

    VA2

    105j90g

    S .

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    :

    VA252

    1 2111

    JZSZ , VA100j2

    1 2222

    IZSZ , VAj1152

    1 2333

    IZSZ ,

    VAj2

    65

    2

    1 2555

    IZSZ , VA52

    1 2666

    IZSZ , VA2

    105j90 ZS .

    , VA2

    105j90g

    ZSS .

    16. ) je 16. O

    4R 4L .

    ) 4R 4L ).(2 ti

    : 200,100 321 RRR , nF501C ,s

    rad105 V4cos2200)( ttu .

    16.1

    ) , : 3241 ZZZZ ,

    111 j CXRZ , 22 RZ , 33 RZ 44

    444

    j

    j

    L

    L

    XR

    XRZ

    .

    , :

    3241 RRXX LC ;

    3241 RRRR ,

    : 2004R 1004LX , mH14

    4 LX

    L .

    ) 2R , , 2112 j RXR

    U

    IC .

    )(tu Vj)1(200 U , A12I ,

    Acos)(2 tti .

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    17. 17, Z

    . : V)j1(10 E , A2J , j)1(51Z ,

    13

    )3j2(102Z ,

    17

    )4j1(203Z , )2j1(44Z j)3(25Z .

    17_____________________________________________________________________________

    17.1 17.2

    Z 17 .

    17.1. 1Z , 3Z

    4Z . :

    S

    20

    8j4

    )2j1(4

    1

    )4j1(20

    17

    j)1(5

    1431ab

    YYYY .

    , je )2j1(1

    abab

    YZ .

    Z )2j1(*abZZ .

    , 0ab )(U ,

    17.2.

    Vj)1(1020 EU ,

    JUZ

    UZZZ

    20

    110

    431

    1111 .

    V)2j1(410 U .

    , 17.2, 0ab)(U V)2j1(410 U .

    a b

    Z , 17.3.

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    Z : A)2j1(2)(

    ab

    0ab

    ZZ

    UI ,

    :

    VA)2j1(102

    1 2 IZSZ

    .

    Z W10Re ZSP . 17.3

    18. 18 : 102 LXR , ,23 R

    5CX , V51E , V2j1112 E 8 . Z .

    18

    ______________________________________________________________________________

    Z , b,

    .

    .

    18.1,

    j)1(4

    j

    )j(

    2

    23ab

    C

    C

    XR

    XRRZ .

    18.1 18.2

    Z j)1(4*abZZ .

    , 18.2, 0ab)(U JRUE C 31 .

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    V11j

    j2

    2

    E

    XR

    XU

    C

    CC ,

    0ab)(U Vj)1(16 .

    Z 18.3

    Aj)1(2)(

    ab

    0ab ZZ

    UI ,

    VAj)1(162

    1 2 IZSZ .

    18.3

    19. 19 : 10CXR , 20LX ,

    Vj2)1(401 E Vj2)1(402 E . Z

    .

    19

    ______________________________________________________________________________

    . 19.1.

    19.1 19.2

    CLCLR

    XXRYYYY

    j

    1

    j

    11ab

    ,

    j)2(41

    abab

    YZ .

    Z j)2(4*abZZ .

    , 0ab )(U ,

    19.2.

    :

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    CCL X

    E

    R

    EU

    XXR jj

    1

    j

    11 2110

    ,

    Vj)1(8010 U .

    , 19.2,

    0ab)(U V40102 UE .

    a b , 19.3.

    Z

    A5.2)(

    ab

    0ab

    ZZ

    UI ,

    VAj)2(5.12

    2

    1 2 IZSZ .

    19.3

    20. 20 : 102 LXR , 53 CXR ,

    V31E , V2j1112 E

    5

    14 . Z

    .

    20

    ______________________________________________________________________________

    .

    , 20.1,

    )4j7(

    j

    )j(

    2

    23ab

    C

    C

    XR

    XRRZ .

    Z )4j7(*abZZ .

    2R

    +E

    3R

    J

    2

    Z

    E

    1

    CX LX

    +

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    20.1 20.2

    , 20.2, 0ab)(U JRIXE C 31 j .

    a I je:

    22 )j( EIXR C ,

    A5

    11jI ,

    0ab)(U Vj)1(14 .

    Z 20.3 :

    Aj)1()(

    ab

    0ab

    ZZ

    UI ,

    : VA)4j7(2

    1 2 IZSZ .

    20.3

    21. 21 ,

    B. : mH1L , srad105 ,21k F1.0 C .

    21 21.1

    ____________________________________________________________________________

    , 21.1.

    :

    mH5.021 LLL

    100LXL 50MXM .

    1I 2I , 2

    21

    III .

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    :

    .2

    2j2j2j2j

    02j2j2j2j

    2121

    1221

    IIIIXXIXX

    IXIXIXIX

    MLML

    MLML

    IIXXI

    XXIXIXU MLMLML 150jj2

    2j2j2j 21

    150jABZ .

    22. 22 : ,221 LL XX 11221 XXRR C ,

    Vj3E .AjJ :) ;

    ) .

    22 22.1

    ______________________________________________________________________________

    22.1 :

    I

    I 1 ; IRIXRJXIX CL 211122 jjj .

    ,

    XXRIXXRR CCL 121221 jjjj , :

    5j2

    jj

    jj2

    1arctanj

    221

    121

    e

    XXRR

    XXRI

    CL

    C , 2

    1arctancos5

    tti

    22j12 4

    j

    1

    eIJI , 4cos221

    tti ,

    2

    cos

    ttj .

    :

    V2j1jj 1211 IXJXU LL V4j1jj 1222 JXIXU LL .

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    :

    VAj22

    1

    2

    1 *11

    JUS LL VA9j22

    1

    2

    1 *22

    IUS LL .

    23. 23 e e

    . : ,112 XXR C ,221 LL XX AjJ .Vj)3( E

    23 23.1

    ______________________________________________________________________________

    23.1 K :

    II 1 ;

    11211 jjj IRJXIXIX LC .

    IRJXIXIX LC 121 jjj ,

    Aj1jj

    jj

    1

    121

    LC

    L

    XXR

    JXXRI ,

    A2j11 II .

    :

    V2j3jj 12111 JXIXU LL Vjjj 11222 IXJXU LL ,

    :

    VA8j12

    1

    2

    1 *111 IUS LL VA

    2

    1

    2

    1 *22 JUS LL .

    24. 24 : 112XXXR LC, 221 LL XX , V3j1E .Vj12 E 1L .

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    24 24.1

    ______________________________________________________________________________

    24.1, :

    11 )j( LL UIXRE ;

    2122 j LLC UUIXE ;

    21 III ,

    :

    212111 jj IXIXU LL 112222 jj IXIXU LL . :

    A1I , Aj)1(1 I Aj2I .

    1L ,

    V)2j1(jj 212111 IXIXU LL ,

    VA)3j1(2

    1

    2

    1 *111 IUS LL .

    25. 25 : ,2,221 CXRR ,

    221 LL

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    B .

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    ______________________________________________________________________________

    2I , 2LX 25.1,

    .

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    IRUE L 111 ,

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    :

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    2

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    26 26.1______________________________________________________________________________

    102112 LL XXkX .

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    :

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    :

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    VA)8j1(1002

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    27. 27 Z,

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    27

    ______________________________________________________________________________ . Z ,

    b, .

    ,

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    , 27.2,

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    Vj13jj)(1120ab

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    28 28.1______________________________________________________________________________

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    2

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    ,

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    ______________________________________________________________________________

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    Z ,

    . a , b, 29.1,

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    30. ,

    A2cos2)( tti , 30. , ,

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    30 30.1______________________________________________________________________________

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    31

    ______________________________________________________________________________

    31 -

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    ,

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    32______________________________________________________________________________

    a)

    11

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    0ul X ,

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    ) ulX .

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    33 33.1

    ______________________________________________________________________________

    ) .

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    111 kLLLk .

    33.1

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    I

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    1

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    34. 34 :

    a) , ulX ;) ;

    ) ulX .

    : mH2.01L , mH1.02L , ,21k nF10C .

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    34. 34.1

    ______________________________________________________________________________

    ) ( 34.1).

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    34 34.2,

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    .

    ) ulX (33.2.).