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4. .

1

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4.1.m = 60 , -

R = 1 M = 120 ,

n1 = 10 -1,

. , —

, ,

. [65,8 .]

4.2.m = 100 r = 12

, , , -

0,8t4 0,5 = 0. -,

t1 = 2,5 t2 = 3 . [3,57 .]

4.3. R = 10 c n = 2

, . A ,

?

8960 3. [34,1 .]

4.4., n = 5 , =

=Wk 60 . . [3,8 · 2 .]

4.5.= 7,2 .

? 10 100 . [4,1 .]

4.6.m = 1 , ,

. = 10 ,

u = 8 . ,

. [2,51 .]

2

4.7., -

= 91 . m = 78 ,

m0 = 3 . -

. [253 .]

4.8. h , -

( ) , «

» R = 0,3 , -? m = 75 ,

m0 = 3 . . [ h = 2R +

+R (1 m0 ) = 7,56 .]

2 m

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4.9. -

A BBYY

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= 0,4 2.

t2 = 25 , t1 = 10

L

2

L t2

= 750 .]

1

= 60 · . [W

1 2

k

2t1

3

4.10. m1

, m2 ,

( . 3.37).

,

F .

t . [Wk F 2 ( t)2 3m1 2m2 ]. 2m1(m1 m2 )

. 3.37

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					A B BYY				c

5

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204

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3.1

3.1.1

1. ( -

) — , ,

, .

-

. 2. ,

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3.-

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4.— .

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— 2 .

5.— , -

, -

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6.,

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7.-

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9.— , -

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10.-

.

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e .

11.— ,

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12.—

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206

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1. , .

2.

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3.

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4. ( ).

3.2

3.2.1

3.2.1.1 .

— , ( -

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x Acos 0t ,

x Asin 0t ,	(4.1)
, 0 , , x	—

, x = 0; – , -

207

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						A BBYY
								; (4.1),

; t = 0, -

. -

(4.1).

0 -

. cos sin) 2 . -

x -, , 2 .

, , :

0 t T 0t 2 ,	(4.2)
	t T ,

	— 2			t . (4.2) ,
	0T 2 ,
	:	2
			.	(4.3)
	0	T

( ) —

, :

	1	.	(4.4)

T

(4.3) (4.4) , 0 , -

, 2

:

0 2 .

(4.5)

, -

, .

, , -

( ) m . ( . 4.1).

l0 ( . 4.1, ). , ( . 4.1, ), -

l . -
0
: mg
	l
Fóïð ,

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208

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Fóïð k l ( k — ). ,

:

mg k l0 .

(4.6)

)

)

)

)

4.1

( ), -

, ( .

4.1, ). X

.

x .

: mg ,

Fóïð k l0 x ( . 4.1, ) -

, Fóïð ). ,

:
Fóïð	mg	Fóïð	(4.7)

X Fx mg k l0 x , -

(4.6) :

Fx kx .

(4.8)

F -

. , ( ) -

, ( ),

. -

F

, . ,

, , .

F , , -

, ( . 4.1, ). -

( ) -

209

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						.A BBYY
									.c		F -
								,

, , . , -

F , -

.

(4.8), F ( X ) -

: ,

x ; , -

( Fx X x -

). F -

.

( ), , ,

, , -

, .

, ( ) -

. -

( ) ma F -

X (4.8):

m d 2 x kx , dt 2

, -

,

	dx	.	d	2	x	..
,		x ,				x .), :
	dt		dt2
						..
						m x kx			(4.9)
(4.9) m									-
:
						x	k	x 0 .	(4.10)

m

k m ,

( ) :

k	2 .	(4.11)
m	0

(4.10) :

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210