: .
, . , , .
l m () .
k. d , (.1).
- j1 j2 , .. .
:
. (1)
j - , M - , e - , I - .
m×g, , f=-k×x, k - . x j1 j2 .1 , d;
x = d×(j2 - j1), f = k×d×(j2 - j1).
:
M = - m×g×l×Sinj - m×g×l×j, (2)
M1 = k×d×(j2 - j1)×d = kd2(j2 - j1) = - M2 .
, . (1) :
(3)
, , , .1. f=k×d×(j2-j1) , .2 f = k×d×(j2+j1).
j1 + j2 = Q1 j2 - j1 = Q2, (4)
. (3), I . :
(5)
(3) , :
(6)
(5) (6) (. . . 1-5-1) .
:
; (7)
m l0×(I = m×l02/3), R m, l (I = m×l2+ m×R2/2, ).
I = m×l02/3 + m×l2 + m×R2/2, (8)
(5) (6), , :
Q1 = ×Cos(wo1×t + a1), Q2 = B×Cos(wo2×t + a2 (9)
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A B Q1 Q2 , a1 a2 - .
(9) (4) j :
j1 = 1/2×(Q1 - Q2) = A/2×Cos(wo1×t + a1) - B/2×Cos(wo2×t + a2) (10)
j2 = 1/2×(Q1 + Q2)= A/2×Cos(wo1×t + a1) + B/2×Cos(wo2×t + a2)
(10) , wo1 wo2, (7), , , (7), wo2 > wo1. (7), . , . . j2 - j1= 0, ().
wo2 > wo1 , , : (. 2).
wk, wo1 wo2. , .. 2×k×d2/I < m×g×l/I, wo1 wo2 , . :
w = wo2 - wo1 n = n2 - n1, (11)
.. w = 2×p×n.
, , , n, n1 n2 , .. . A= f(n) .
.3.
1 . 2, 3 4. 5 6 . 7, .
8 9. 10, 11, - , .
, , 7, 10, 11 6, .
12. 13, . 14, .