:
x = A cos(ω t + φ0),
x , , ω , φ0 , t .
T = .
:
υ = = A ω sin (ω t + φ0),
a = = A ω2 cos (ω t + φ0).
, : E k = = sin2(ω t + φ0).
:
E n = cos2(ω t + φ0).
T = ,
m , k ,
T = ,
l , g ,
T = ,
I , , m , l .
: l np = ,
, .
:
A = A 12 + A 22 + 2 A 1 A 2 cos(φ2 φ1)
: φ = arctg .
1, A 2 , φ1, φ2 .
:
+ cos (φ2 φ1) = sin2 (φ2 φ1).
:
x = A 0 e - β t cos(ω t + φ0),
β , , , 0 . t :
A = A 0 e - β t .
:
λ = ln = β T,
: T = .
:
D = .
:
y = y 0 cos ω(t ),
, 0 , ω , t , , , υ .
+ , X, , .
:
λ = υT,
υ , T .
:
y = y 0 cos 2π ( + ).
:
y = (2 y 0 cos ) cos ω t.
. ,
x = n ,
,
x = (n + ) .
20
50 , 4 . ) ; ) t =0 t = 1,5 ; ) .
|
|
x = a cos(w t + j0).
. w = . :
) x = 0,05 cos( t + ).
) x t = 0.
x 1 = 0,05 cos = 0,05 = 0,0355 .
t = 1,5 c
x 2 = 0,05 cos( 1,5 + )= 0,05 cos p= 0,05 .
) x =0,05cos ( t + ) :
. 1(0) 2(1,5), . , D t = 4 c , D t = 2 c . 0.
21
. 2 , 50 , . , 25 .
1 . :
x = 0,05 cos p t,. . w = = p.
t:
υ = = 0,05cos p t.
, 0,025 :
0,025 = 0,05 cos p t 1,
cos p t 1 = , p t 1 = . :
υ = 0,05 p sin = 0,05 p = 0,136 /c.
2 . :
E = ,
, w , m .
E k = , E = , k = m w2, , E = .
:
= + ,
: a 2w2 = υ 2 + w2 x 2,
υ = w = p = 0,136 /c.
22
= 2 , = 3∙10-7 . F = 2,25∙10-5 ?
, , : E = . (13)
x :
F = k x (14)
(13) m w, (14) k. m k:
w2 = ,
k = m w2 F = m w2 x. m w2 (13) : m w2 = , F = x.
x: x = .
:
x = = 1,5∙10-2 = 1,5 .
23
. 1 = 3 2 = 4 . , : 1) ; 2) .
1) , :
A = ,
1 2 , j1 j2 . , j2 j1 = 0, cos 0 = 1.
:
A = = = 1+ 2 = 7 .
2) , :
|
|
cos(j 2 j 1) = sin2(j 2 j 1).
j2 j1 = 0, cos 0 = 1, sin 0 = 0, : =0,
=0,
.
x . , MN. : A = = 5 .
24
=4 , l = 1,6, . t = 4,5 . 1) ; 2) .
1) :
x = A 0 e -b t cos2p .
0 b.
:
l = b .
b = = = 0,4 -1.
, :
4,5 = A 0 cos 2p = A 0 cos = A 0 .
:
A 0 = 4,5∙ () = 7,75 .
:
x = 0,0775 cos t.
2) x = 0,0775 , .
25
, t = 1 ? l = 1 .
: l= b ,
b , . :
w0 = = 3,13 -1.
: A 0 = A 0 e -b t,
b t = ln2 = 0,693,
b = = 0,0116 c-1.
b << w0, w = b w0 : T = = 2 c.
b :
l = b T = 0,0116 -1 ∙ 2 = 0,0232.
26
x = 4 sin600 p t .
, l = 75 , t = 0,01 . υ = 300 /.
, : x = 0,04 sin 600 p(t ).
:
t = 0,01 = 0,0075,
600p ∙ 0,0075 = 4,5p,
sin 4,5p = sin = 1.
, x = 0,04 , .. l =75 t = 0,01 c .
1. .. . .: , 2001.
2. .. . .: , 1998.