同济大学大学物理.pdf

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1、 1 振动学基础 1 Oxy j t i t r 2 2 5 2 SI A B C D B 2 r s C A a t d d v B v t r d d C v t s d d D a t d dv C 3 A B C D B 4 (A) (B) (C) (D) D 5 H h v (A) v H h H B v h H H (C v H h D v h H B 6 0 v t v H h v 5 2 (A) g t 0 v v (B) g t 2 0 v v (C) g 2 1 2 0 2 t v v (D) g 2 2 1 2 0 2 t v v C 7 kt e 0 v v k v 0

2、 0 t (A kt e k x 0 v B kt e k x 0 v C ) 1 ( 0 kt e k x v D ) 1 ( 0 kt e k x v C 8 A B 2 m s -1 A Ox B Oy A A B A (SI) A 2 2 i j B 2 2 i j C 2 2 i j D 2 2 i j B 1 Ox 3 2 2 3 t t x SI v = 1.5 m s -1 2 Oxy 8 4 , 6 2 t y t x SI t = 1 s t a = 6.4 ms -2 n a = 4.8 ms -2 3 R = 1 m s t 2 2 2 t s a 0 45 s = 2

3、.5 m 4 Ox a = 3+2 t (SI) v 0 = 5 m s -1 3 t s v = 23 m s -1 5 , 2 6 t t x (SI) t 0 4s _8m_ t 0 4s _10m_ 6 R t = 0 P Bt A v ( A B ) P t a = 3 B n a = B R A 4 2 7 3 1 . 0 t s (SI) 2m v 30 m s -1 6 m s -2 _450 m s -2 _ 8 0 v 1 v Ox 0 v Oy 2 0 2 0 1 2v v v gx x y 1 Oxy 4 3 2 1 5 3 2 t t y t x ( x y m t

4、s ) (1) t (2) (3) t =1 s t =2 s (4) t = 4 s 1 j i 4 3 2 1 5 3 2 t t t r m 2 4 3 2 1 5 3 2 t t y t x t 18 11 7 9 4 18 1 2 x x y 3 j i 5 . 0 8 1 r m j i 4 11 2 r m j i 5 . 4 3 r m 4 1 x s m 3 d d t x v 1 y s m ) 3 ( d d t t y v s 4 t 1 x s m 3 v 1 y s m 7 d d t y v j i 7 3 v m s -1 0 d d x x t a v 2 y

5、 y s m 1 d d t a v j a m s -2 2 -1 s m 150 2 v 0005 . 0 SI 4 Ox ) 0005 . 0 ( 2 v g a x t a d d d d v v v ) 0005 . 0 ( d d 2 v v v g x max h 0 v v v v 2 d 0005 . 0 d 0 150 0 max g x h m 52 . 764 max h 3 0.10 m 3 4 2 t SI 1 t = 2 s 2 3 t t R a R a n d d d d 2 1 t =2 s , v = 4.8 m s -1 a n = 230.4 m s

6、-2 a t = 4.8 m s -2 a = 230.5 m s -2 (2) rad s t a a a n 15 . 3 66 . 0 2 2 2 s t a a n 55 . 0 4 0 v 0 v Ox Oy 0 t 1 t 2 t (1) 2 0 2 1 , gt y t x v 2 0 2 / 2 1 v g x y (2) v x = v 0 v y = g t 2 2 2 0 2 2 t g y x v v v v Ox = tg 1 ( gt /v 0 ) 2 2 2 0 2 / /d d t g t g t a t v v v 2 2 2 0 0 2 / 1 2 2 /

7、t g g a g a t n v v t a x y O 0 v t a n a g 5 1 (A) , (B) , (C) , (D) C 2 P PC P A A B B C C D D 3 70kg 6 g (A) 10 N (B) 70 N (C) 420 N (D) 4100 N D 4 Oxy 25 . 0 kg i F t N 0 t 1 s m 2 j v O A j i t 2 2 2 m B j t i t 2 3 2 3 m C j t i t 3 4 3 2 4 3 m D B 5. 1 m 2 m 1 m 2 m a g m F 1 1 m a A a a B a

8、a C a a D P A B C 2 O m 2 m 1 m 2 F 5 6 B 6 m M (A) g (B) g M m (C) g M m M (D) g m M m M (E) g M m M C 7 A F A F (A) sin (B) cos (C) tan (D) cot ( C ) 8 R (A) gR (B) gR (C) gR 2 (D) M B 1 2 kg 8 20 t F N Ox 0 t 3m s -1 3 4 5 2 t t v 2 M 0 v f v v k f k k M x 0 v 3 m a a g a ma 2 4 m A A gcot 5 0.4

9、0.04 g 0.25 g m M 6 F 7 A 4 A 7 6 R m 2 g R 7 M 0.6 h 1.5 m l l h / sin 2.92 m 8 g a 2 1 A B m A 3mg / 4 1 ( ) 1 m 2 m 2 a T m2 2 a m1 a1( ) 1 1 1 a m T g m 1 2 2 2 a m g m T 2 2 1 2 a a a 3 2 1 2 2 2 1 1 ) ( m m a m g m m a 2 1 2 1 2 ) 2 ( m m m m a g T h M l R m 6 7 8 1 8 2 1 2 1 2 1 2 ) ( m m a m

10、 g m m a 2 m l m 1 F 1 2 1 0 0 0 1 0 T T ma T F a m T 1 m m F a 1 F m m m T 1 1 0 2 O O x dx x l m m d d a m T T T ) d ( d x a l m T d d 1 x l m m mF T d ) ( d 1 l x F T x l m m mF T d ) ( d 1 ) ( ) ( 1 x l l m m mF F T T x 3 R , m , (1) v , 2 m F m 1 R v 3 T + dT T dm 1 dx O x m 1 a T 0 m F T 0 a 9

11、 (2) v 3 v 1 v R v 2 m R v 2 m f t ma f t ma m R v 2 R v 2 t a 2 R v t v 2 d d t a v v R t 2 d d 3 v v 2 v v R d d 0 t t v R t 2 4 m R m mg N f s m, x R m N N 2 sin cos y mg N N cos sin / g R 2 sin cos sin cos sin cos sin cos 2 2 R R g g sin cos cos sin 2 2 R g R g R m 4 10 1 A B m A m B m B 2m A KB

12、 KA E E (A) 2 1 (B) 2 / 2 (C) 2 (D) 2 D 2 20 g 400 m s -1 980 g (A) 2 m s -1 (B) 4 m s -1 (C) 7 m s -1 (D) 8 m s -1 ( B ) 3 A B L E K (A) L A L B E KA E kB (B) L A =L B E KA E KB (D) L A L B E KA E KB ( C ) 4 Oxy ) ( 0 j i F F y x (0 2R F (A) 2 0 R F (B) 2 0 2 R F (C) 2 0 3 R F (D) 2 0 4 R F B 5 m 0

13、.5 kg Oxy t x 5 2 5t y SI 2 t s 4 t s A m B m 1 v 0 30 2 y x O R 4 11 (A) 150 J (B) 300 J (C) 450 J (D) -150 J B 6 m M G R 1 R 2 (A) 2 R GMm (B) 2 2 R GMm (C) 2 1 2 1 R R R R GMm (D) 2 1 2 1 R R R GMm (E) 2 2 2 1 2 1 R R R R GMm C 7 M m l A (A) 0 (B) gl 2 (C) M m gl / 1 2 (D) m M gl / 1 2 C 8 1 2 3

14、A 1 (B) 1 3 (C) 1 2 (D) 2 3 B 1 m v v v m 2 2 A B 4 0 rad s -1 15 1 r cm C 5 2 r cm 36 rad s -1 3 700 m s -1 , 7 C A B 2 12 500 m s -1 100 m s -1 4 1 m kg Ox x F 2 3 (SI) 3 m W 18 J x 3 m v 6 m s -1 5 k m k g m 2 2 2 6 250 kg 500 kg 2 25t F N 3 0.9 ms -1 0.45ms -1 7 k m O F P E k mg F 2 ) ( 2 8 m 3

15、/ r k r F k r 0 r r 0 2 mr k F k m 7 x O 1 13 1 , L M t x dt x d ( L x M / d ) dx/dt t t x x d d d d , d d d d 2 v t t x x F t x d d v F = F 2 2 ) d d ( d d d d v L M t x L M t t x x F L Mgx F gx / 2 , 2 2 v L Mgx G G G F F 3 2 m 0 v R m N t m N 2 d d v v 0 0 d d v v v v e 0 v v ) 1 ( 2 1 2 1 2 1 2

16、2 0 2 0 2 e m m m W v v v 3 L h ( h 3 m v 0 2 14 0 P E 2 0 h hg L m E 2 2 1 2 L mg m E v dy y L L mg fds A L h f ) ( 2 ) ( 2 h L L mg : 0 E E A f ) ( ) ( 2 2 2 h L h L L g v 4 M m v 0 h v 1 mgh V M m m V M m m 2 2 0 0 2 1 2 1 v v M m g M h 2 2 0 v 2 V 2 2 2 0 0 2 1 2 1 2 1 V M m m V M m m v v v v 0

17、v v M m M m m v0 M 4 h y O 15 1 m G G C D C 2 A B C D C 3 OA O (A) (B) (C) (D) A 4 A B C D D 5 (A) (B) (C) (D) B 6 J 0 3 1 J 0 3 1 3 1 C 3 D 3 O m G 1 O A 3 16 C 7 m l A 2 B 2 C D 2 B 8 l m 4 l O A l g 7 3 4 B l g C l g D l g 12 A 1 t 20 sin 20 SI 0 t 400 rad s -1 8000 rad s -2 2 30cm -2 s rad 5 . 0

18、 240 t a = 0.15 m/s 2 n a = 1.26 m/s 3 M l m O A C M m gl m M 3 ) 6 3 ( 0 v B mg M m M m T 3 7 15 O M l C A B 0 v 3 l/4 O 8 7 17 4 J = 2.0 kg m 2 0 M = -7.0 N m 8 0 0 = 14 rad s -1 5 R m a J = a R a g m 2 ) ( 6 J t = 0 0 M k ( k 0 ) 0 3 1 = 0 2 0 2 9 k J J k 0 3 1 t = 7 M R 0 M u t 2 2 2 0 2 2 t u R

19、 R 8 m M R v R m M m ) 2 ( 2 v 1 r m r r 2 m m 2 O O 2 / 9 2 mr J m A B 10 r cm 1 2 A 40 h cm m m m O r r m B A 1 18 1 r a r a mr Tr r T ma T mg ma mg T 2 2 9 2 B A 2 2 s rad 3 . 10 1 . 0 19 8 . 9 2 19 2 r g 2 A h r h 2 2 1 s rad 08 . 9 1 . 0 4 . 0 3 . 10 2 2 r h 2 A B 1 m 2 m m r B A m m m , , 2 1

20、r a mr r T r T m a m g m T m a m T g m m 2 2 1 2 2 2 2 1 1 1 1 2 1 m A B 2 m 2 m 1 m A B m 2 m 1 g m P 1 1 1 T 1 T 2 T 2 T g m f 2 19 g m m m m m a 2 2 1 2 1 g m m m m m m g m T 2 2 1 2 1 1 1 1 g 2 m m m m m m g m T 2 1 2 1 2 2 2 3 m 1 r 1 A O 1 m 2 r 2 B B O 2 A B A B ) ( 2 2 1 1 2 m m g r m t 1 2

21、2 2 1 1 r r - 1 2 2 2 2 2 1 2 1 1 1 2 1 2 1 r m fr r m fr g m f 1 t t 0 2 2 1 1 t r m g m t r g 2 2 1 2 1 1 1 1 2 1 ) ( 2 2 1 1 2 m m g r m t 4 m l AB m A 1 A 2 1 2 2 2 2 1 3 4 3 1 ml ml ml J J J B A m 4 A O 1 O 2 B 3 20 2 2 2 1 sin 2 sin J l mg mgl l g sin 2 3 1 A B C D Q t 0 2 2 Q t Q 2 d d Q D 2

22、A B C D B 3 A B 4 C 0 D 2 C 4 k m T 1 m/2 T 2 A 2 1 T B 1 T C 1 T /2 D 1 T / 2 E 1 T /4 C 5 A 2 A O x A B C D A / 2 /2 A O O A O O O A O x x x x A/2 A/2 -A/2 -A/2 5 O A k x v 2 21 B 6 A 62s . 2 B 40s . 2 C 42s . 0 D 382s . 0 B 7 A 2 kA B 2 kA /2 C 2 kA /4 D 0 D 8 T Ox A T/4 B T/12 C T/6 D T/8 B 1 2

23、A _ 2 A= cm 2 T= 4s = 1 - s 2 = 2 3 x = ) 2 3 2 cos( 02 . 0 t m v = ) 2 3 2 sin( 01 . 0 t -1 s m a = ) 2 3 2 cos( 2 01 . 0 2 t -2 s m s 3 t 3 3 10g 1 s 1000m 99kg . 4 3 k x O v x/m 6 t/s 1.0 4 2 0 2 O x/cm 2 2 4 t/s 22 1 2 m N 10 8 0.158 m 0.5 s 2 4 cm 2 A Ob A 0 t Oc A t a x = ) 4 1 cos( 02 . 0 t m

24、_ b x = ) 4 3 cos( 02 . 0 t m_ 5 x 1 x 2 _ 3 2 6 T 2 / 0 T t t = 8 T T 8 3 7 2 3 2 8 _ 0 d d 2 2 2 x t x A/2 7 x/m A t/s 2.0 x 1 x 2 4.0 O x x O O A A c c b b (b) (a) t t 4 3 4 4 5 O x x 1 t x 2 23 1 kg 258 . 0 m Ox k=25N m -1 1 T 2 cm 2 A t = 0 cm 1 0 x Ox 0 v 3 (1) s 638 . 0 84 . 9 2 2 , s 84 . 9

25、258 . 0 25 1 - T m k (2) m/s 17 . 0 3 sin 02 . 0 84 . 9 sin , 3 0 A v (3) ) 3 84 . 9 cos( 02 . 0 ) cos( t t A x m 2 A T 0 t 2 0 A x 1 2 a b 3 0 t a b 1 ) 3 2 cos( 3 t T A x 2 0 a 2 b 3 6 2 3 3 T T t a 12 5 2 2 3 T T t b 3 a , b, T ) 1 ( 2 2 x gL gxL f a 2 x t b A O t=0 weizhi A x O 0 x a weizhi b we

26、izhi b zhi x a b O L f 24 m k , 1 2 gL k a gL mg 2 a g a L gL m k 2 2 g a T 2 2 a b A 4 1 1 2 1 s 3 A 0 cm 5 2 cos 4 3 2 4 3 cos 2 2 2 2 1 2 1 2 2 2 1 A A A A A 13 . 53 3 4 tg 2 4cos 3cos0 2 4sin 3sin0 tg cos cos sin sin tg 1 1 - 2 2 1 1 2 2 1 1 1 0 A A A A 0 0 2 10 3 3 cos 5 2 1 t x x x cm (2) 3 1

27、x x x k 2 1 (k = 0, 1, 2, ) 0 1 k 2 (k = 0, 1, 2, ) 8 5 3 3 1 A A A cm (3) 3 2 x x x 1 2 2 k (k = 0, 1, 2, ) 2 2 2 3 2 2 1 2 k k (k = 0, 1, 2, ) 1 5 4 3 2 A A A cm 4 O x t x 3 cos 3 1 cm 2 3 cos 4 2 t x cm t x 3 cos 5 3 cm 1 2 3 1 1 2 1 s 3 A 0 cm 5 2 cos 4 3 2 4 3 cos 2 2 2 2 1 2 1 2 2 2 1 A A A A

28、A 25 13 . 53 3 4 tg 2 4cos 3cos0 2 4sin 3sin0 tg cos cos sin sin tg 1 1 - 2 2 1 1 2 2 1 1 1 0 A A A A 0 0 2 10 3 3 cos 5 2 1 t x x x cm (2) 3 1 x x x k 2 1 (k = 0, 1, 2, ) 0 1 k 2 (k = 0, 1, 2, ) 8 5 3 3 1 A A A cm (3) 3 2 x x x 1 2 2 k (k = 0, 1, 2, ) 2 2 2 3 2 2 1 2 k k (k = 0, 1, 2, ) 1 5 4 3 2 A

29、 A A cm _ 1 500Hz 1 s m 360 3 A 0.24m B 0.48m C 0.36m D 0.12m D 2 A 2 B C D C 3 s 5 . 0 t 1 s m 10 u P A 10 cos 10 x t y cm B 10 cos 10 x t y cm -10 x /m y /cm 10 0 P 10 20 3 26 C 10 cos 10 x t y cm D 10 cos 10 x t y cm B 4 4 2 1 I I A 4 2 1 A A B 2 2 1 A A C 16 2 1 A A D 4 1 2 1 A A B 5 A B C D D 6

30、 P 1 S 1 1 S P 1 r 2 S 2 2 S P 2 r k P A k r r 1 2 B k 2 1 2 C k r r 2 2 1 2 1 2 D k r r 2 2 2 1 1 2 D 7 3 4 20 100 cos 10 0 . 2 2 1 x t y SI 0 x A 3 20 100 cos 10 0 . 2 2 2 x t y SI B 3 4 20 100 cos 10 0 . 2 2 2 x t y SI 1 S 2 S P 1 r 2 r 6 27 C 3 20 100 cos 10 0 . 2 2 2 x t y SI D 3 4 20 100 cos 1

31、0 0 . 2 2 2 x t y SI D 8. (A) 100 10000Hz (B) (C) (D) C 1 A B B A 3 A B 0.5m 100Hz _3_m u _300_ 1 s m 2 Ox 3 10 2 m 0.01s 1 s m 400 0 t Ox y (SI) ) 2 2 200 cos( 10 2 3 x t y 3 t y 2 1 sin 06 . 0 SI 1 s m 2 5m (SI) ) 4 5 2 sin( 06 . 0 t y 4 T u u T 5 S x t A y 2 cos w S S w 2 6 s 1 T A _10cm _ _20cm

32、u 10 1 s cm T 2s _ 0.5 1 s y 2 3 10 cos 10 x t cm s 5 . 0 t 0 t 6 -10 y/cm x /m 10 0 10 20 28 7 1 S 2 S 1/4 1 S 2 S 2 0 I 1 S 2 S 2 S _ 4I 0 _ 1 S _0_ 8 0.5s 1 h km 60 5 629 1 s m 340 1 1 s m 20 u Ox A t y 4 cos 3 (SI) : 1 A 2 A 5m B 1 (SI) ) 20 ( 4 cos 3 ) ( cos x t u x t A y 2 (SI) ) 20 5 ( 4 cos

33、3 ) ( cos x t u x t A y 2 , 0 t 250Hz P 1 2 100m 1 ) ( cos u x t A y -1 s m 50000 250 200 500 250 2 2 m 01 . 0 u A cos 0 0 A y x t cos 1 2 2 2 2 cos 4 4 (SI) 4 ) 50000 ( 500 cos 01 . 0 x t y 2 100 x (SI) ) 4 5 500 cos( 01 . 0 4 ) 50000 100 ( 500 cos 01 . 0 t t y u B A x 1 S 1 S 2 /4 7 2 2 y /cm -1 1

34、00 x /m O 2 P 1 29 (SI) ) 4 5 500 sin( 5 4 5 500 sin( ) 500 ( 01 . 0 d dy t t t v 3 1 S 2 S t y 2 cos 1 . 0 10 cm t y 2 cos 1 . 0 20 cm P cm 50 S , cm 40 S , s cm 20 2 1 1 - P P u 1 2 P 3 P 1 cm ) 20 ( 2 cos 1 . 0 1 x t y cm ) 20 ( 2 cos 1 . 0 2 x t y 2 ) 4 2 cos( 1 . 0 ) 20 40 ( 2 cos 1 . 0 1 t t y

35、 P ) 4 2 cos( 1 . 0 ) 20 50 ( 2 cos 1 . 0 2 t t y P 0 3 P 4 t x y 750 cos 16 . 0 cos 2 1 2 3 3 10 2 t s cm 0 . 5 x 1 t T x A y 2 cos 2 cos 2 1 - 3 s cm 10 7 . 4 s 750 2 750 2 cm 3 . 39 16 . 0 2 cm 0 . 1 T u T T A 2 cm 6 . 19 2 x 3 1 - 3 s cm 10 04 . 1 750 sin 750 39 . 1 t t y v S 1 S 2 P 3 30 _ 1 A

36、B C q F E q q F D ( C ) 2 Q S q A S e B S e C S e D S e ( D ) 3 q A abcd A 0 6 q B 0 12 q C 0 24 q D 0 48 q ( C ) 4 R R S Q q 2 a A a b c d q 3 31 5 Q P R O r A 0 B 0 2 C 0 4 D 0 8 ( C ) 5 R Q r R r P A 0 E r Q V 0 4 B 0 E R Q V 0 4 C 2 0 4 r Q E r Q V 0 4 D 2 0 4 r Q E R Q V 0 4 B 6 A C B C A B C D

37、 ( D ) 7 +Q 0 q A B C D B C D +Q (A) A B (B) A C (C) A D (D) ( D ) 8 (A) (B) (C) 7 D C B +Q A E E E E C A B C A B C A B C A B 6 32 (D) ( C ) 1 0 2 E E , 2 0 E , 2 3 0 E , 2 0 2 R ) 0 ( Q Q S S E 4 0 2 16 R S Q 3 q d W qd A 0 2 4 O x i E bx b a 1 S 1 b a 3 2 2 S 2 0 Q b a 3 0 5 R Q 2 1 2 S R O y z a

38、x 2 S z 1 S z a O 4 O x 6 y 2 a -a 2 a a + 33 r P P V = R r Q 1 1 4 0 6 2 a x 2 a x O y 2 2 0 4 2 a y a Ox 7 +Q 1 r 2 r R 2 1 r R r E 2 0 4 R Q 0 V R Q 0 4 2 0 4 r Q 8 q +Q R 3/4 a d 0 d R qQ 0 4 1 R q q dq = d d R l 2 R q 2 0 4 d d R R E 8 R +Q a d +q -q R O 1 -dq +dq x y dE + dE - O 34 2 0 4 d d R

39、 R E E Ox 0 2 0 2 0 2 0 0 2 4 d cos 2 cos d 2 R q R R E E E y y 2 b b x kx 0 k 1 1 P 2 P 2 P 3 1 E S 0 d q S S E 0 2 0 0 0 0 2 d d 1 2 kSb x x kS x S SE b b 0 2 4 kb E 2 P S E 0 2 x 0 0 2 d kSx x x kS S E E , 2 2 2 2 0 b x k E b x 0 3 0 E 0 2 2 2 b x 2 b x . 3 R 4 R qr R r q 0 r R x a O . b 2 P P x

40、1 P 2 P x S S E E x dx S S . b E E 35 1 2 3 1 4 3 4 2 / d 4 / d 4 d d R r qr R r r qr V q q r r R q V Q R V 0 3 4 d / 4 d 2 1 r 1 0 4 0 4 1 2 4 0 1 2 1 d 4 1 4 r R qr r r R qr E r 4 0 2 1 1 4 R qr E R r 1 2 r 0 2 2 2 / 4 q E r , 2 2 0 2 4 / r q E R r 2 3 3 3 1 0 2 0 4 0 2 2 1 1 4 12 d 4 d 4 d d 1 1

41、R r R q r r q r R qr U R R r R R r r E r E 1 r R 2 0 2 0 2 2 4 d 4 d 2 2 r q r r q U r r r E R r 2 4 2cm 0.134mm 850V 1 R 2 R r 1 R r 2 R 0 2 rE , r E 0 2 1 R r 2 R 1 2 0 0 12 ln 2 d 2 d 2 1 2 1 R R r r r E U R R R R 1 2 12 ln R R r U E 1 1 6 3 2 3 1 2 1 12 1 m V 10 54 . 2 2 10 134 . 0 2 10 2 ln 2 1

42、0 134 . 0 850 ln R R R U E 2 1 4 3 2 2 1 2 2 12 2 m V 10 7 . 1 2 10 134 . 0 2 10 2 ln 2 10 2 850 ln R R R U E 36 _ 1 A B C D ( D ) 2 R 0 U r A 3 0 2 r V R B R V 0 C 2 0 r RV D r V 0 ( C ) 3 A B C D ( B ) 4 d 2 d A B C D 3 q 37 ( D ) 5 A B r B A A E B B E A A E B E B A E B E C A E B E D A E B E ( D )

43、 6 A (B) C (D) ( B ) 7 R d R d q O A 0 B d q 0 4 C R q 0 4 D R d q 1 1 4 0 ( D ) 8 1 d 2 d 1 2 2 1 8 1 2 2 d 1 d 7 +q R O d A B 5 38 A 2 1 d d B 1 2 d d C 1 D 2 1 2 2 d d B 1 q q 2 q q 2 1 r 2 r r = 2 2 2 1 r r 3 d 0 V 3 d V = 0 3 2 U 4 B Q A S d B AB V 4 S Qd 0 2 B AB V S Qd 0 5 1 R 2 R r D= r 2 E=

44、 r r 0 2 6 0 Q r 1 P 2 P 1 q 2 q S S 4 d +Q A B 6 P 2 P 1 r 1 r 2 r O 39 1 1 r OP 2 2 r OP 1 P D 2 1 0 4 r Q 2 P D 2 2 0 4 r Q 1 P E 2 0 0 1 4 r Q r 2 P E 2 2 0 0 4 r Q 7 S 1 Q 2 Q A B C D A s Q Q 2 2 1 B s Q Q 2 2 1 C s Q Q 2 2 1 D s Q Q 2 2 1 8 r r 1 r r 1 a b S d U 0 q c a b c a b c c 1 q 2 q 2 1

45、 q q q 1 a 1 q b 2 q c c U a c 2 1 d E U U c 7 S 1 Q 2 Q B A B D C d/2 d/2 d c b a 0 V 1 40 a c S q E 0 1 1 2 0 1 d S q U U c c U U d S q 0 1 2 2 c b 2 0 2 d S q U c c U d S q 0 2 2 3 2 3 1 c q S d U U c 0 2 2 1 2 a d a d 2 A B + Ox x P ) ( 2 2 0 0 x d x E a d a a d a x x d x U U d ) ( 2 2 d 0 0 B A

46、 l E a d a a d x d x a d a ln ln ) ln( ln 2 0 0 0 d a) a d U U C ln 0 B A 3 q R +q r 1 2 3 3. 1 q q r q R O 3 A B d x x o P 41 O q E q E E E E O 0 O E O r r r q ( 4 2 0 E E O q (2) O U U U U O U U q q r q U 0 4 U = 0 r q U O 0 4 (3) 1 q r q R q U 0 0 1 4 4 0 r qR q / 1 4 Q S d 1 r 2 r 1 2 3 1 1 2 2

47、2 1 1 d E d E 2 1 E E , 1 0 1 1 r E 2 0 2 2 r E 2 1 2 1 r r Q S S 2 2 2 1 S Q r r r ) ( 2 2 1 1 1 S Q r r r ) ( 2 2 1 2 2 2 E P r n 0 ) 1 ( ) 1 ( ) ( 2 ) 1 1 ( 1 2 1 1 1 1 r r r r S Q ) 1 ( ) ( 2 ) 1 1 ( 2 2 1 2 1 2 r r r r S Q 1 r 2 r 4 42 3 d S C r 2 1 0 1 , d S C r 2 2 0 2 ) ( 2 2 1 0 2 1 r r d S C C C 1 m 10 4 3 T 10 0 . 7 5 1 7 0 A m T 10 4 (A) 0.14A B 1.4A C 14A D 2.8A B 2 l d i O O z P x y z Ox (A) 0 (B) 2 3 2 2 2 0 ) ( d 4 z y x l iy (C) 2 3 2 2 2 0 ) ( d 4 z y x l ix (D) ) ( d 4 2 2 2 0 z y x l iy B 3 B R S S n B S (A) B R 2 (B) B R 2 2 (C) sin 2 B R (D) cos 2 B R P y i x z o r 2