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A B BYY

. ( .

-

).

1.?

2.?

3.( ) -

?

4., -

, ?

5.,

?

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2 « »

1..

. ( -

, -

.

, x(t) .)

2.. (

, -

, ).

3.. (

. -

).

4.. (

.

, -

.)

1.-

?

2.?

?

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?

5. ,

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I( )

1.?

2.?

3.?

4., , -

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5..

6.. .

7..

8..

9., -

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10.?

11.,

.

12.,

?

13.?

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14., -

.

15..

16..

17., , -

.

18.?

19..

20., .

21.? ?

22.? .

23.? -

.

II( )

1.-

.

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242

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		A
. .
3.	.
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4.
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5.	,

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11..

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1.,

, .

2.-, : x a cos( 0t ) .

3.-, : x Asin( 0t ) .

, .

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4.2

»

4.2.1 .

.

1 ( 1)

-

A = 8 , t = 1 n = 120

45°.

:	:
A = 8 = 8 · 10-2
t = 1 = 60	:

n = 120				x(t) Acos( 0t ) ,
45				0 — ,
	4							2		,				T		t		.
x(t)	—?				0			T								n
				0 :
						2 n						2 120
															4 .
				0			t							60
				x(t) 0,008cos(4 t															) .
														4
				: = 0,008 cos ( 4 t									) .
							4

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244

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2 ( 2)

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m =10 -

= 0,2 . 5 . : 1)

, ; 2) -

.

	:	:
	m = 10 = 10-2	:
	= 0,2					X Acos( 0t 0 )
	A = 5 = 0,05
	Fmax — ?				dx				A sin( t											) ,
	W — ?																	0
					dt							0			0
				a		d			A2 cos( t								0		) .
						dt									0
		, , -
		F ma A 2m cos( t																			0	) ,
												0			0
		F Fmax a amax , . cos( 0t 0 ) 1 .
		, , 0 2 ,
		F	A 2m 4 2 2Am .
		max		0
		:
		W Wk Wï					Wkmax					Wï màx .
			1							kA2			mA	2	2
		W		m 2											0	, k m 2 .
			2	max			2					2										0
		,

W mA2 4 2 2 2 2 A2m 2 . 2

Fmax 4 2 0,05 10 2 0,8 .

W 10-2 0,05 2 2 0,04 19,7 .

: 0,8 ; 19,7 .

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1 ( 1).

A = 4 T = 2 .

, -

x = 2 . [ x = 0,04 cos ( t			) .]
0	3
	2 ( 2).

,

(t) 6sin 2 t .

[ x(t) = 3 cos 2 t .]

4.2.2

. . -

1 ( 1)

,

:

x		A cos	2			(t ) ,
	1	1		T		1
x	2	A cos		2		(t	2	) ,
		2		T
A1 = 3 ; À0 = 2 ; 1 = 1/6 ;						2 = 1/3 ;			T = 2 .

.

:

x1 A1 cos 2 (t 1 ) T

x2 A2 cos 2

T

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246

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A1 = 3 ;

A2 = 2 ;

1 = 1/6 ;

2 = 1/3 ;

T= 2 .

xf (t) — ?

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. 4.14

-

. -

t = 0.

: x Acos( 0t ) ,

:

		x1				A1 cos(								2					t					2				1 ) ,
															T										T
				x		2	A cos(								2			t				2					2		) .
									2						T								T
,
2																					T		. 1- 2- -
							2						0				2
										,			2										2		.
		1					T		1								T
:
								2				2				-1 = 3,14 -1.
					0				T				2
	2		1		=30º,															2					2					1	= 60º.
1	2	6																							2				3

A1 A2 : A1 1 = 3

X 30º, A2 2 = 2 60° . -

A , A1 A2 :

A A1 A2 .

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A A12 A22 2 A1 A2 cos( 2 1) .

-

( . 4.14):

arctg A1 sin 1 A2 sin 2 . A1 cos 1 A2 cos 2

:

A 32 22 2 3 2 cos(60 30 ) = 4,84 .

arctg		3sin 30 2sin 60		arctg0,898 = 42º = 0,735 .
		3cos 30 2 cos 60
	,
,	,
x Acos( t ) , A = 4,84 ;			= 3,14 -1; = 0,735 .
0			0

2 ( 1).

, -

1 2 5 1 2 3 . -

A 1 0 ,1 A2 0,05 .

-

:

x2		y2		2xy	cos(	2	) sin2	(	2	) .	(1)
A12		A22		A1 A2			1			1

2 1 0 , (1) :

x2 y2 2xy 0 ,

A12 A22 A1 A2

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248

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x

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A2

A B BYY

c

y

x

0

,

A

A

A

1

2

1

. ,

.

tg A2 A1 0,5, . 26 34 .

,

A A12 A22 11,2 . , -

l 11,2sin(10 t ) .

3

1( 1).

4 5 . -

4

, -

, .

[ x = 9,24 cos ( t ) ].

2 8

2 ( 1)

, -

, -

x Acost cos 45t ( t — ). :

1);

2). [1) 1 = 46 -1; 2 = 45 -1;

2)T = 6,28 ].

4.2.3, .

1 ( 1)

, l , -

n1 = 10 , n2 = 6 -

. l1 l2 .

249

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:

l = 16 = 0,16 n1 = 10

n2 = 6

t1 t2 t

l1 — ? l2 — ?

:

-

:	T 2			l .
				g
,		T	t	.
:			n
t 2		l1 (1),
n1		g
t 2	l1 l		(2).
n2		g
(1) (2):
n2	l	l1 .
n		l
1	1

:

0,36 =		l1		,	l1 0,36t1 0,0576 .
	l1
		0,16
			l1 = 0,09 ( )
			l2		= 0,25

: l1= 9 l2 = 25 .

2 ( 2)

l = 30 :

, — . -

, .

Lïð T .

.
:				:
l	= 0,3
m1	m2 m			:

AB

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250