Физика-КР4

-

.

- , -

.

-

. -

.

x1(t) x2(t) , - + , << .

, -

.

x(t)=x1(t)+x2(t)=Acos t+Acos( + )t -

x(t)=[2Acos( /2)t]cos t ( -

/2 ).

. -

,

x(t) ,

A -

:

	A	2Acos		t
			2

T =2 / .

.

-

, .

,

. -

“ ”

. -

-

x x 02 x 0

(2.27)

x(t) A0 e tcos( t 0 ) 02 2

(2.28)

T 02 2

0

. -

21

A(t)=A0e- t.

ln	A(t)	T	(2.29)
	A(t T)

:

= / Ne =1/ , Ne=1/ .

-

0 -

. , L, C, R - -

, (2.27) (2.25), ,

	0			1			R	(2.30)
							2L
				LC

.

- “ -

”.

.

U(t)=Umcos t. ,

(2.25)

Q Q 0			Q	Um	cos( t)	(2.31)
		2

L

(2.28) -

, -

, -

“ ” . , -

	Q(t) Qmcos( t )					(2.31)
		Um
Qm				tg		(2.32)
					02 2
	L 02 2 )2 2 2

Qm

, . =0 (2.33)

Qm(0)=Um/(L 02)=CUm, . ,

Um ( ).

>> 0 : Qm( )=Um/(L 2) 0 . p (

) . Qm ,

:

22

				Um					0		(2.34)
	p	02 2	Qm p )				Qm (0)
				L2 02 2				1 2 02

(2.34) , -

Qm( p)= Qm(0).

-

-

.

.

, . -

, ( ). -

- , -

, , -

( ).

V,

x=0 -

(0,t)=Acos t. (x,t)

=x/V,

. , -

(x, t) Acos( co x/V]) Acos( t k x)

(2.35)

-

k=2 / , =V T=2 V/ .

, , -

.

, :	1=Acos( t-kx),
2=Acos( t+kx).
	(2.36)
1 2 2Acos(k x) cos( t)

, -

x. x= m /2, m=0, 1, 2, ..., -

2Acoskx , 2A. -

. ,

, . -

23

x= (m+1/2) /2, m=0, 1, 2, ... . , -

, .

3. .

1. , .3, I=10.0

. ,
R=10.0 , =60 .
:	A		3	1	I
I=10.0 ,
R=10.0 = 10 10-2 ,	C			2	B
=60 , 0=4 10-7 .	2				1
______________________			O
.
:			.3

,

. : 1

2 3. ,

,

(2.3), (2.5). .

= /3, 1= 0 I/(12 R). (2.5) 2. ,

1=30 , 2=90 , = R sin 1=R/2,

. B2 3 /(4 ) 0 I/R . 3 ,

1= 2=0, 3=0. ,

	B = B 1+ B 2. -

.

, -

dB ( . (2.2)), ,
.				-
			dB , B 1, -
“ ”, B 2 - “ ”. ,
				| BO | | B2 B1 |

| 3 /(4 ) 1/12 | 0 I/R . : = 6.90 .

2. a=10 , -

I=100 ,

=1.0 . , -

24

,

, : 1) 1= 90 ; 2) 2= 3 .

.

:

=1.0 , I=100 , a=10 =0.10 ,

1= 90 , 2= 3 .

_________________

1, 2

: (2.9),

(2.10).

. =0, , =0, . -

pm B . -

, (2.10)

. -

. -

,

d : dA= M d .

(2.10) m (2.9), dA= I B a2 sin d . -

,		:
A I B a 2 0 sin( )d .		90 :
A I B a 2 ( cos ) | / 2	I B a2 . -
0

, 1=1 . 2 -

2= 3 = 3/180= /60 . -

sin A2 I B a2 0 2 d I B a2 22 / 2 . ,

2= 1.37 .

, -

(2.15): =I .

1, , ( . (2.13)) = S cos0 =B a2.

90 2=0.

, . 1= -I = -I 2 1)= I a2, .

3. , U=400, =1 . -

25

R n -

. -.

:

U=400 , =1000 , me=9.11 10-31 , qe=1.6 10-19 , 0=4 10-7

___________________________________

R n

: R -

: -

F (2.12). ,

, .

, F =m an, n - , -

V R

: n=V2/R. , q V B sin = m V2/R , ,

=90 , R=m V/(q B).

m V :

m V 2 m T , , ,

, -

U: T=q U. -

( . (2.1)),

R=(2 U m/q)1/2/( 0 H)= 5.37 10-2 .

,

: n=V/(2 R). -

, n=q 0 H/(2 m)= 3.5 107 c-1.

4. =0.1 -

n=10 -1 , N=103 ,

.
S=150 2. -			n
i, -
0=30 ,		S	t
<Ei>, -
			B
1=0 2=90 .			I
:
=0.1 , n=10 -1, N=103 ,
S=150 2=0.015 2,		.4
0=30 , 1=0 , 2=90 .
________________________

26

i < i>

: i

(2.16). -

(2.14) , Ei=-N /dt.

( .4) ,

t,

(t)=B S cos( t), ,

(2.13); -

t. ,

Ei=N B S sin( t).

=2 n. n

t= 0,

Ei=N B S 2 n sin( 0). Ei= 47.1 .

< i> ,

t, < i>= - / t= -N / t.

= 2 1= -B S (cos 1-cos 2); t,

, t= ( 2- 1)/(2 n).

, < i>= 2 n B S (cos 1-cos 2)/( 2- 1)= 60 .

5. -

N=1200 , .

I=4 =6 . -

L W .

:

N=1200, I=4 , =6 .

_______________________

L W

: L, , -

=L I; , , -

(2.14).

L=N /I. -

W=L I2/2 ( . (2.21)), ,

, W=N I/2. : L=1.8 , W=14.4 .

6. ,

l=1.0 ,

d=3.0 . , N=1300 ,

27

, =1.0. , -

.

:

l=1.0 , d=3.0 =0.0030 , N=1300, =1.0 .

________________________

I, w , w

: ,

. -

, -

, .

S , -

:

=1 . ,

.

=1 / 0= 8.0 105 . -

, .8: =4.2 102 .

(2.22),

: w /2= 4 105 3, w /2= 2.10 102 3.

-

(2.19) : L Hl dl i Ii . -

, -

. L, ,l , l , : H c (l d) H d N I . I= 2.0 .

7. , -

x1=A1cos([2 /T][t+ 1]), x2=A2cos([2 /T][t+ 2]),

1= 3 , 2= 2 , 1= 1/6 , 2= 1/3 , = 2 .

-

.

: (2.24,) x1=A1cos( t+ 0), = 2 /T= -1

1= 2 1/T, 2= 2 2/T .

1= /6 = 30 , 2= /3 = 60 . -

.

t=0. -

28

1= 3 2= 2 1= 30 2= 60

= 1+ 2 ( , .2),

. -

-

(2.26). -

: = 4.84 , = arctg0.898= 42 . -

x(t)=4.84cos( t+0.735) .

8. -

t= 5 10-3 40%

. N= 103

. ,

, R= 10 .

, -

Um=12

= 0.9 p?

: Q(t)= Q0e-t, = R/(2L).

t, = (1/t)ln(Q0/Q(t))= (103/5)ln(10/6) 102 -1. -

L= R/(2 )= 10/(2 102)= 0.05 .

(2.28)	(2.30), ,
			. : T=
T 2		1/LC 2

t/N= 5 10-6 . ,

= 1/ = 0.01 . , 2 -

1/LC. , T LC C= (1/L)T2/(4 2)= (100/5)(5 10-6)2/(4 3.142) = 51 .

= T, =(1/N)ln(A0/AN), N= 103, AN= 0.6A0. = 5 10-4.

-

(2.33), (2.34) Uc= Q/C:

	Uc			Um				Um
			LC 02 2 )2 2 2				LC p2 2 2 )2 2 2

2=(0.9 p)2= 0.81 p2,

	Uc			Um
			LC (0.19 2p 2 )2 2 0.81 p2

29

, (1/(LC))= 0= p2+2 2. , -

02>> 2. , -

, Uc(0.9 p)= Um/(0.192)= 330 .

9.

V= 20 . , x1= 12x2= 15 , = 0.75 .

,

t= 1.2 , -

= 0.1 .

: , -

, = 2 ; , -

x, -

= x 2 / = 2 (x2-x1)/ .

, = 2 (x2-x1)/( ), , , = 8 .

: T= /V= 0.4 , = 2 /T= 5 -1. -

(2.35),

(x,t)=0.1cos(5 (t-x/20)) .

, -

t: 1= 0.1cos(5 (1.2-12/20))= -0.1

, 2= 0.1cos(5 (1.2-15/20))= 0.071 .

4.

.

5

, .

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