工程测试技术基础 张春华 课后答案[1-5章].khda

- 66 7.8 10 /1.01825447.6601682/10 6 0.00003/25.048941.197655/10 0.026/5.4824.743 6 6 7.8 10 /1.01825447.6601682/107.8 10 /1.01825447.6601682/10 6 6 0.00003/25.048941.197655/100.00003/25.048941.197655/10 x s Xxx n 8 1 802.44 8 i i x x 8 2 1 () 0.040356 8 1 i i xx s 0.014268 8 x s 10 1 i i LL 2 10 2 1 0.6mm i LL i i L L dhV 2 4 d h V 2 222 2 2222 22 22 24 2 Vdhdh dh VVdhd dh VV dh 22 22 44(0.5%)(0.5%)1.1% Vdh Vdh 0.6mm0.6mm d d 1- 4 0 t x(t) T0 2 T0 2 0 T A - A T0 0 0 (0) 2 ( ) (0) 2 T At x t T At 00 000 0 0 0 22 0 2000 2 111 ( )d =d +d =(cos- 1) ( =0, 1, 2, 3, ) TT jntjntjnt T Tn cx t etAetAet TTT A jnn n 00 1 ( )(1 cos) jntjnt n nn A x tc ejne n =0, 1, 2, 3, n (1 cos) ( =0, 1, 2, 3, ) 0 nI nR A cn nn c 22 2 1, 3, , (1 cos) 00, 2, 4, 6, nnRnI A n A cccn n n n 1, 3, 5, 2 arctan1, 3, 5, 2 00, 2, 4, 6, nI n nR n c n c n 000000 =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) TTTTTT 000000 111111 TTTT 111111 =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) d +d +cx t etAetAetcx t etAetAet 000000 d +d +d + 222222000000000000000000 TTTTTT 111111111111 0000002222000000222200000000022 111111 22222222 111111111 22222222222222222222222222222222222222222222 0 d =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) =(cos- 1) ( =0, 1, 2, 3, ) jntjnt cx t etAetAetcx t etAetAet 000000d d jnt 000000000 jntjnt cx t etAetAetcx t etAetAet 000000 jntjnt 000000000 cx t etAetAet 0 ( )(1 cos)( )(1 cos)( )(1 cos)( )(1 cos) 000000 n ( )(1 cos)( )(1 cos)( )(1 cos) 00000000 (1 cos)(1 cos) ( =0, 1, 2, 3, ) ( =0, 1, 2, 3, ) (1 cos)(1 cos) |cn| n /2 -/2 0 03050 3 050 2A/ 2A/3 2A/5 2A/5 2A/3 2A/ -0- 30- 50 -0- 3 0- 50 0 ( )sinx txt xrms x 0000 2 2 0 0 000 224211 ( )dsindsindcos T T TT x xxxx x ttxt tt tt TTTTT 2 222 00 rms0 000 111 cos2 ( )dsindd 22 TTT xxt xx ttxt tt TTT ( )(0,0) at x tAeat (2) 22 0 22 0 (2) ( )( ) (2)2(2) ajf t jf tatjf t eAA ajf X fx t edtAeedtA ajfajfaf 22 ( ) (2) k X f af Im( )2 ( )arctanarctan Re( ) X ff f X fa f |X(f)| A/a 0 (f) f 0 /2 -/2 TTTTTT 000000 ( )(0,0)( )(0,0)( )(0,0)( )(0,0)( )(0,0)( )(0,0)( )(0,0) jf tatjf tjf tatjf t222222 X fx t edtAeedtAX fx t edtAeedtA jf tatjf tjf tatjf tjf tatjf t222222 X fx t edtAeedtAX fx t edtAeedtA jf tatjf tjf tatjf tjf tatjf tjf tatjf tjf tatjf t2222222222222222 ( )arctanarctan Re( ) ( )arctanarctan 0000 d 00 2 x x 00000000 t 00 t ttt t t d t ttt tt 000000 d d 000000 t ttt t t d d (2)(2) (2)2(2) (2) eAAeAA (2)(2) X fx t edtAeedtAX fx t edtAeedtA (2)(2)(2) eAAeAA (2)(2)(2) eAA X fx t edtAeedtAX fx t edtAeedtAX fx t edtAeedtAX fx t edtAeedtA (2)2(2) 22 (2) 22 (2) Im( )2Im( )2 ( )arctanarctan( )arctanarctan Im( )2Im( )2Im( )2Im( )2Im( )2Im( )2Im( )2Im( )2Im( )2Im( )2 ( )arctanarctan( )arctanarctan t sgn(t) 0 1 - 1 t u(t) 0 1 1- 251- 4 a)b) 10 ( )sgn( ) 10 t x tt t 1 0 ( )sgn( ) 0 at at at et x tet et 1 0 ( )sgn( )lim( ) a x ttx t 0 222 11 22 0 4 ( )( ) (2) jf tatjf tatjf t f Xfx t edte edteedtj af 1 0 1 ( )sgn( )lim( ) a X ftXfj f F 1 ( )X f f 0 2 ( ) 0 2 f f f 222222222222 Xfx t edte edteedtj 222222atjf tatjf tatjf tatjf t222222 Xfx t edte edteedtjXfx t edte edteedtj atjf tatjf tatjf tatjf tatjf tatjf t222222222222222222222222222222222222222222222222222222 Xfx t edte edteedtjXfx t edte edteedtj 222222atjf tatjf tatjf tatjf t222222222 0 0 atjf tatjf tatjf tatjf t222222 Xfx t edte edteedtjXfx t edte edteedtj 0 0 atjf tatjf tatjf tatjf tatjf tatjf t222222222 Xfx t edte edteedtjXfx t edte edteedtj atjf tatjf tatjf tatjf tatjf tatjf t 0 0 222222 Xfx t edte edteedtjXfx t edte edteedtjXfx t edte edteedtj 0 0 atjf tatjf tatjf tatjf t222222 Xfx t edte edteedtjXfx t edte edteedtjXfx t edte edteedtjXfx t edte edteedtj atjf tatjf tatjf tatjf tatjf tatjf t222222222222222222atjf tatjf tatjf tatjf t222222222222222222222222222222atjf tatjf tatjf tatjf tatjf tatjf t222222 1 1 X ftXfj( )sgn( )lim( ) f X ftXfj( )sgn( )lim( ) 1( ) sgn( ) at x tet t x1(t) 0 1 - 1 f (f) 0 /2 0f |X(f)| -/2 10 ( ) 00 t u t t 11 ( )sgn( ) 22 u tt 1111111 ( )( )sgn( )( )( ) 22222 U fu ttfjfj ff FFF 2 2 11 ( )( ) 2 U ff f f |U(f)| 0 (1/2) f (f) 0 /2 -/2 10 ( )( )d 00 tt u t t 11111111111111 2222222222 ( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( ) 11111111111111 ( )( )sgn( )( )( )( )( )sgn( )( )( ) 1111111 ( )( )sgn( )( )( ) 1111111 ( )( )sgn( )( )( ) 11111111111111 2222222222 ( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( ) 111111111111111111111 ( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( ) 111111111111111111111111111111111111111111 ( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( )( )( )sgn( )( )( ) 1111111111111111111111111111 ( )( )sgn( )( )( ) 1111 ( )( )d( )(0) ( )( ) 222 t U ffffj jff F 0 cost 0 cos ( ) 0 ttT x t tT 0 ( )( )cos(2)x tw tf t ( )2 sinc(2)W fTTf 00 22 0 1 cos(2) 2 jf tjf t f tee 00 22 11 ( )( )( ) 22 jf tjf t x tw t ew t e 00 00 11 ( )()() 22 sinc2()sinc2() X fW ffW ff TT ffTT ff f X(f) T f0- f0 0 ( )sin at x tet 1- 26 t tT- T T- T x(t) w(t) 1 0 0 1 - 1 00000000 sinc2()sinc2()sinc2()sinc2()sinc2()sinc2() 000000 sinc2()sinc2()sinc2()sinc2()sinc2()sinc2() 000000000000 sinc2()sinc2()sinc2()sinc2()sinc2()sinc2() 00000000 sinc2()sinc2() 000000 X(X f f ( ( ( ) ) f f f T - - T T x(t) 00 0 1 sin() 2 jtjt tee j 00 1 ( ) 2 jtjtat x teee j 1( ) (0,0) at x teat 11 22 0 1 ( )( ) j tatj t aj Xfx t edteedt aja 00 1010 2222 00 222 000 22222222 0000 ()()11 ( )()() 22()() ()2 () () () () ajaj XXX jj aa aa j aaaa 0 0 X( ) - ( ) 00 cos() m t 0 cost 0 ( )cosf tt 0m 1 1 ajaajaajaajaajaajaajaajaaja 222 1111 222 22()()22()() 2222 22222222 22222222 00000000 ()()()()11 22()()22()() 22222222 ()2()2 222222222222 00000000 ajajajaj()()()() 22()()22()()22()() 22222222 22()()22()()22()() j ()2 ajajajajajaj()()()() 22222222 ajajajaj()() 22()()22()() 2222 jj aajj aajj aa22()()22()()22()()22()()22()()22()()22()() 222222222222 ()()()() ()2()2()2()2()2()2 00000000 () () () () () () () () () () () () 222222222222 () () () () () () () () () () () () () () () () 0000000000000000 1- 271- 7 F( ) 0 f(t) 0t -m m 0 ( )( )cos()x tf tt ( ) ( )Ff tF 00 0 1 cos() 2 jtjt tee 00 11 ( )( )( ) 22 jtjt x tf t ef t e 00 11 ( )()() 22 X fFF f X(f) 0 -0 0m 0 ( )sin()x txt x 2 x 0 0 00 0 11 lim( )dsin()d0 TT x T x ttxtt TT 0 2 T 0000 ( )()()( )()() 00000000 ( )()() 0000 ( )()()( )()()( )()()( )()()( )()()( )()() 0000000000 ( )()()( )()()( )()()( )()() 00000000 ( )()()( )()()( )()() 0000 X X( (X X X f f ( ( ) ) f f f 00 22 2222 00 0 000 00 111 cos2() lim( )dsin ()dd 22 TTT x T xxt x ttxttt TTT 012 2 x Tttt 0 00 2 ( )lim xx T TTt P xx txx TTT 2200 00 0 ( )22 d1 ( )limlim d xx P xx txxtt p x xTxTx xx x(t) x x+ x tt t 1 ( ) 1 H s s 1 ( ) 1 H j 2 2 11 ( )( ) 2 1 () 1 () AH T 1 100%A 58.6%1s 32.7%2s 8.5%5s T T T 1 ( ) 10.005 H j 2 1 ( ) 1 (0.005 ) A( )arctan(0.005 ) 0101 2 1 (10)0.50.499 1 (0.005 10) yAx 1 (10)arctan(0.005 10)2.86 0202 2 1 (100)0.20.179 1 (0.005 100) yAx 2 (100)arctan(0.005 100)26.57 ( )0.499cos(102.86 )0.179cos(10071.57 )y ttt 1 ( )( ) 1 (0.005 ) ( )( )( ) 1 ( ) 151 H s s 1 ( ) 1 H j 2 1 ( ) 1 () A 2 1 ( ) 1 100%1100% 1 (2) A f 262 11 1100%1100%1.3% 1 (2)1 (2523 1050)f 6 ( )arctan(2)arctan(2523 1050)9.33f 22 ( ) s X s s 22 1 ( )( )( ) 1 s Y sH s X s ss 2 111111 ( ) 1 1 ()2(1)2(1) Y s jsjjsj s ( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100% 1111 1 (2523 1050)1 (2523 1050) ( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100%( ) 1 100%1100% 2 ( ) 1 100%1100% 2 1 (2)1 (2)1 (2) ( ) 1 100%1100%( ) 1 100%1100% 1 (2)1 (2)1 (2)1 (2)1 (2)1 (2)1 (2)1 (2)21 (2)1 (2)1 (2)1 (2)1 (2)1 (2) 262626 1111 262626 1 (2523 1050)1 (2523 1050) 2626262626 1 (2523 1050)1 (2523 1050)1 (2523 1050) 2626 ( )arctan(2)arctan(2523 1050)9.33( )arctan(2)arctan(2523 1050)9.33( )arctan(2)arctan(2523 1050)9.33( )arctan(2)arctan(2523 1050)9.33( )arctan(2)arctan(2523 1050)9.33 1 2 22 / 2 2/ 2 111 ( ) ( ) 1 ()2(1)2(1) 1() 1 ()21 () 1 cossin 1 () 1 1 () cos(arctan) 1 () t j tj t tj tj tj tj t t t y tY seee jj eejee e tte te L 1 1 1.53 ( ) 3.50.57171 K H s sss 22 2 2 2222 41 ( ) 1.41.4 nn nnnn K Hs ssss 2 22 ( ) 2 n nn H ss 2 22 1 ( ) 12 nn A 2 2 ( )arctan 1 n n 2 22 1 ( ) 12 nn A f ff ff 2 2 ( )arctan 1 n n f f f f f 2222 22222222222222222222 nnnn2 2 nnnnnnnn 2222222222 2 2nnnnnn2 2 K K 222222 2nnnnnn2 nnnnnnnn 1.41.41.41.4ssssssssssss1.41.41.41.41.41.4 2222222222222222222222222222 1.41.41.41.4 222222222222 ssssssssssss1.41.41.41.41.41.4 nnnn 2 222222 n n nnnn ssssssssss 22222222 nn ss nnnnnn 2222 ssss 2222 2 22 ssss2 2 2222 ssssss 2222 ssssss 22 0 11 0.215 11 ln(1.5/3)ln(/)M Kx 2 2 1 1.024rad/s 1 1 0.215 d n 2 222 33.15 ( ) 20.441.05 n nn H s ssss 2 222 33.15 ( ) 21.050.44 n nn H jj 2 22 3 ( ) 10.44 nn A 2 2 ( )arctan 1 n n 2 22 3 ()6.82 10.44 n nn A ()90 n 3.15 21.050.4421.050.44jjjj21.050.4421.050.4421.050.44 2 21.050.4421.050.44 2 2222222222 10.4410.4410.4410.44 nnnnnnnn n n 3 3- 843- 4 1.5V 2 00 2 2 NAdL S d 2 00 2 2 NAdZ S d 3- 843- 843- 43- 4 T 0000 2 00000 12326 3 2 153 () 8.85 101(4 10 ) ( 1 10 ) (0.3 10 ) 4.94 10F4.94 10 pF AAAA C 3- 853- 8 x xp RL ue uo Rx Rp xpl p x RRk xx x e e o (1)1(1) p ppp LpLpp x u x u u xRR xxx xRxR xx oe p x uux x P e e (1)1(1)(1)1(1) p ppp (1)1(1)(1)1(1) LpLppLpLpp u xRR ppp xxxx (1)1(1)(1)1(1)(1)1(1) RxR xxRxR xx (1)1(1)(1)1(1)(1)1(1) LpLppLpLppLpLpp (1)1(1)(1)1(1)(1)1(1)(1)1(1)(1)1(1)(1)1(1)(1)1(1) LpLpp oeoe x x uuxuux oeoe uuxuuxuux o1234e 1 () 4 URRRR U R 66 oee 11 2 2 1033 10 V3 V 44 g R UUSU R 66 oee 11 2 2 1036 10 V6 V 22 g R UUSU R 63 oee 11 2 2000 1033 10 V3mV 44 g R UUSU R 63 oee 11 2 2000 1036 10 V6mV 22 g R UUSU R o / U S R R o R US R o / / U Uo R R R RR R 2 2000 1036 10 V6mV 6363 2 2000 1036 10 V6mV 63 ( )(cos10cos100 )sin10000 1 sin(10 10000)sin(10 10000) 2 1 sin(100 10000)sin(100 10000) 2 sin10010sin9990sin10100sin9900 22 oegeg g g gg R uuSt uSAtBt Et R S EAtt S EBtt S EAS EB tttt f9900 An(f) 9990 1001010100 2 g S EB 2 g S EA 2 g S EB f0 An(f) 1500f8500 An(f) 9500 1000011500 20 30 100 100 10 15 10500 15 10 An(f ( ) ) f 2020 21 2 cc ff 012cc ff f 3 2 C R i(t) ui(t) uo(t) RC 1 ( ) 1 H s s 1 ( ) 1 H j 1 ( ) 0.0011 H s s 1 ( ) 10.001 H j 2 1 ( ) 1 (0.001 ) A( )arctan0.001 2 12 (1000) 1 (0.001 1000)2 A (1000)arctan0.001 1000 4 o 10(1000)sin1000(1000)5 2sin(1000) 4 uAtt 5 2 4 Ci i( (t t) ) RCRC uo o( (t t) ) j j j j 0.00110.00110.00110.0011 ( )( )H H( ) 1 ( ) 1 H j 2 1 ( ) 1 () A( )arctan 2 1 (10)0.894 1 (0.05 10) A(10)arctan(0.05 10)26.6 2 1 (100)0.196 1 (0.05 100) A(100)arctan(0.05 100)78.7 R1 C1 uo(t) 4- 464- 12 C2 R2 ui(t) 1 2 1 2123 ( ) ()1 s H s ss 1 2 1 2123 ( ) ()1 j H j 1 2 2 2 1 2123 ( ) 1() A 2 1 2 123 1 ( )arctan () R1 1 R R2 i i( (t t) ) 4- 464- 124- 12 u uo o( (t) C2 1 2123 ()1()1 1 21231 2123 ()1()1 1 21231 2123 ()1()1()1 1 2123 ()1 1 2123 1 1 ()1 j j j j ()1()1 - 50 - 40 - 30 - 20 - 10 0 10 1 100101102103104 - 90 - 45 0 45 90 Bode Diagram Frequency(rad/sec) 2 i 2 i1i1 dd d() d() InABnAB U rtr RRtr RR 2 i1i1 22 22 i1i1 ()()( ) ( ) ( )2 1 ()() n inn nABnABr Kr RRr RRIs H s InABrnABr U sss ssss rr RRI r RRI n r I i1 1 ()2 nAB RRIr i1 () nAB K r RR 4 1 3 i1 100 10150 7.5rad V ()10(12575) nAB K r RR 4 53 i1 11100 10150 23.717 ()(12575)2 2 2.5 1010 nAB RRIr 1 5 10 20rad s 2.5 10 n r I i i i1i1i1i1 d() d()d() d() i1i1i1i1i1i1 InABnABInABnAB U Ui i d() d()d() d()d() d() i1i1i1i1i1i1i1i1 d() d()d() d() i1i1i1i1i1i1i1i1 10 i1i1i1i1 ()()()() i1i1i1i1 ( )2( )22222 ()() nABnAB r RRr RR()()()()()() i1i1i1i1i1i1 InABrnABrInABrnABr ( )2( )22222 ssssssss ( )2( )2( )2 rr RRI r RRIrr RRI r RRI()() ()()()()()()()() i1i1i1i1i1i1 ( )2( )22222 ssssssssssss ( )2( )2 4 53 i1 11100 10150 0.7 ()(12575)2 2 2.5 1010 nAB RRRRIr 7500 2006576.3 0.72.5 R 4 1 3 i1 100 10150 0.221rad V ()10(125756576.3) nAB K r RRR (0,0) ( ) 0(0) at eta h t t () 0 1 ( )( ) () 2 ata ta h Rh t h tdteedte a 11 22 12 1212 1112 2122 1 ( )lim( )( ) ()() 2 11 lim( )()lim( )() 22 11 lim( )()lim( )() 22 ( )( )( )( ) T x TT TT TTTT TT TTTT xx xx xx Rx tx tx tx tdt T x t x tdtx t x tdt TT x t x tdtx t x tdt TT RRRR 1 2( ) 0 x x R 2 1( ) 0 x x R 1 1 1 11 1 111111 0 1 2 1 11111111 0 12 1 1111 00 1 22 11 11 1 0 1 ( )cos()cos() 1 cos()cos() 2 cos 22cos() 2 0cos()cos() 22 T x T TT T RAtAtdt T A ttttdt T A tdtdt T AA t T 1 2 2 2 ( )cos() 2 x A R 12 22 12 12 ( )( )( )cos()cos() 22 xxx AA RRR 1212 ( )( )( )( )( )( )( )( ) 121212 TT222222 ( )( )( )( )( )( )( )( )( )( )( )( ) 22222222222222 2122212221222122 22 21222122 22222222222222 2122 ( )0( )0( )0( )0( )0( )0 111111 ( )cos()cos()( )cos()cos() 111111111111111111111111 ( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos() 111111111111111111 1 2222 1 0cos()cos()0cos()cos() 111111 11 2222 1111 0cos()cos()0cos()cos() 1111 T1 22 1 AAAAAA 222222 1 111111111111 0cos()cos()0cos()cos()0cos()cos() 11111111 11 0000 lim( )()lim( )()lim( )()lim( )()t x tdtx t x tdtt x tdtx t x tdtlim( )()lim( )()lim( )()lim( )()lim( )()lim( )()lim( )()lim( )()lim( )()lim( )() 111111111111 ( )cos()cos()( )cos()cos() 111111111111 ( )cos()cos()( )cos()cos()( )cos()cos() 111111111111111111 ( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos()( )cos()cos() 111111111111111111 ( )cos()cos()( )cos()cos()( )cos()cos() 111111111111 TTTTTTTT 11 0000 t y(t) t x(t) 1 - 1 1 T - 1 5- 245- 3 sin( t) 0 0 00 3 44 3 0 44 11 ( )( ) ()() ( ) 1 ( 1)sin()1 sin()( 1)sin() 2 sin() TT xy TT T TT Rx t y tdtx ty t dt TT tdttdttdt T 411 ( )coscos3cos5 35 y tttt 00 0 00 114 ( )( ) ()sin()cos() 41 sin()sin() 2 2 sin(2)sin() 22 0sin()sin() TT xy T TT Rx t y tdtttdt TT ttttdt T tdtdt T T T 0 3 44 3 0 44 1 ( )( ) () 1 ( 1)sin()1 sin()( 1)sin() 2 sin() T xy TT T TT Rx t y tdt T t dtt dttdt T Rx t y tdtx ty t dtRx t y tdtx ty t dt( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( )( )( ) ()() ( ) 3TTTT3 4 4 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 444444 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 444444 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 4444 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 444444 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 444444 ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() T T ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() TTTT 0000 T ( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin()( 1)sin()1 sin()( 1)sin() 411411 ( )coscos3cos5( )coscos3cos5 411411 ( )coscos3cos5( )coscos3cos5 411411 ( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5 3535 ( )coscos3cos5 35 ( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5( )coscos3cos5 114114114114 ( )( ) ()sin()cos()( )( ) ()sin()cos() 0000 ( )( ) ()sin()cos()( )( ) ()sin()cos() 0000 ( )( ) ()sin()cos() 114114 ( )( ) ()sin()cos() 114114114 ( )( ) ()sin()cos()( )( ) ()sin()cos() 114114114114 ( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos()( )( ) ()sin()cos() t y(t) t x(t) 1 - 1 1 T - 1 sin( t) 0 0 t y(t+ ) 1 - 1 0 4 T3 4 TT T3 4 T 4 T 4 10 2 4 ( )3 2 ()0, 1, 2, y y T T T RT T RnTn Ry( ) 0T T/2 3 3 4 4 T T ()0, 1, 2,()0, 1, 2,()0, 1, 2, T ()0, 1, 2,()0, 1, 2, T ()0, 1, 2,()0, 1, 2,()0, 1, 2,()0, 1, 2,()0, 1, 2, Rx( ) 0 T Rxy( ) 0 x(t)y(t) 5- 255- 4 00 11 lim( ) ()lim( ) () TT TT x t x tdtx t y tT dt TT 1 11 00 2 1111 0 2 1111 0000 2 11 ( )lim( ) ()lim( )() 1 lim( )()( )() 1 lim( )()( )() 00( ) TT xxx TT T xxx T TTTT xxx T xxx Rx t x tdtx tx tdt TT x tx tx t x tdt T dtx t dtx tdtx t x tdt T R 1 2 ( ) x R 1 lim( )0 x R 2 lim( ) xx R lim( ) x RC x C TT00 11111111 0000 ( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )() 0000 1111 ( )lim( ) ()lim( )()( )lim( ) ()lim( )() 111111111111 ( )lim( ) ()lim( )()( )lim( ) ()lim( )()( )lim( ) ()lim( )