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:

:


: ( ) .

: , , .

1. .

1.1.  .

, . , . , , . .

, , . - , . :

1)    , , , ;

2)    .

x(t)=A cos(w0t+j0) (1a)

x(t)=A sin(w0t+j0), (1)

x(t)- t, , A- , , w0- () j = (w0 + j0) - t, j0 - . x t. +1 1, x +A A. , , T, . T 2, .. (w0(t+T)+j0))-(w0t+j0) = 2.

T = 2/w0. (2)

, :

v = 1/T, (3)

, , . (2)(3),

w0 = 2v. (4)

(): 1 , 1 .

x(t) ( v a) :

dx/dt = v(t) =-Aw0sin(w0t+j0) = Aw0cos(w0t+j0+p/2) (5a)

(5)

.. , . (5) (5), , Aw0 Aw0. (5) (1) /2, (5)- . , , x=0, v=dx/dt . x - + max , a=dx/dt + - .

(5)

(6)


, x=Acos(w0t+j0). (6) (1).


1.2

X , . x t - (1):

x(t)= Acos(w0t+j0). (5) (5) v(t) a(t) : v(t)=A w0 cos(w0t+j0+p/2), a(t)=Aw0 cos(w0t+j0+p).

F=ma, m, x(t) a(t)

F=-m w0 x. (7)

, .

, ,

(8)

(8)

, ,

(8)

(8)

:

(9)

(7) (8) , 2w0 . (9) , .

1.3.

, , .

1.3.1

, , (.1).

, (e = M/J, e - , M , , J ) F

(10)

M = Ftl=-mgl sina =-mgla, J- , , l- , Ft = -mg sina== -mga g .

(10)

(11)

(12)

(13)

(14)

:

(15)

(15) , w0

(16)

L=J/(ml) .

' , L, (. .1). , , =l . : , . , .


 



`P=m`g

. 1

1.3.2.

, m, , .

J =ml, l- . , , , , (16), .

(17)

(16) (17) , , , . , , .


l

m

.2

1.3.3

2, 3 1, (.3). . , 4.

T = 2p J/mgl (. (16)) g. T, l , J g. , , , l J . , l , .

3


4


1

3

1

x

.3

, J l g. . -, (.1)

J = Jc + ml (18)

Jc , , l- . (18) (16),

(19)


, , l . l =- mgl sina (.1), , . l 0, : . (19): l 0

(20)

, l , Jc ml l. = l . l T Tm=Tmin, . T(l) .4.

l=0 . , , (19), T(l) . T(l) , .

T


T

Tm

lm l1 0 lm l2 l

.4

, , . l1 l2(l2=l1) (.5), :

T(l1) = T(l2). (21)

(19),

Jc/ml1+l1= Jc/ml2+l2 (22)

l1 = l2,

l2 = Jc/ml1 (23)

(24)

,

(24)

(24), g : L=(l1+l2) ( ) l1 l2, , l1¹l2. , .. T(l1)=T(l2)=T. , L=(l1+l2) .


L

.5

2.

2.1.

: . .

(.6) 2, 5. 8. 1 . 11, 10. , , . 3 . , , , . , , , .

11

10

9

6

8

4

7

l 6

5

4


3

2

1

.6

. 9, 4 6. . 6. ( 1,0) . .

, , (4 6)

2.2.

2.2.1.

, . .7 l = l0 + r, r . : h 2r. , , l = H-h-r. T1 T2 : l l. (17)


l l0 H


2r


h

.7

:

, g .

l-l=h-h. .

2.2.2.

1. .

2. h .

3. ( 4-5), , . t1, n=50 . 50 l . 1.

4. l. h . t2, n=50 . 50 l . 1.

5. t T1 T2 T= t/n. T1 T2.

6. . 1. 1.


/ h, h,젠 n t1,t2,񠠠 T1,T2,c T1,T2,񠠠 g,/


2.3. .

, . , , , . .., , . .

. , , . . . , , . , .

1. :

1-2 , . .

2. . ( 4-5), , .

t, n=50 . 2.

3. . 2.

4. , , 1 2. 2.

5. 3 4, 1 , 9-10 .

6. . .

7. , . . , . (T=T1=T2).

8. (16) .

2

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x, 젠 t0, 񠠠 T1, 񠠠 t2,񠠠 T2, 񠠠



2012 , .