x = A - ,
x ,
, ,
- , ,
- , t = 0,
- ,
( , , 2 ),
- , , = 1/T,
V = dx/dt = A + ) ,
a = d2x/dt2 = -A 2 + ) .
:
x1 = A1 + , x2 = A2 + ),
A = - .
tg = (A1sin +A2sin ) / (A1cos +A2cos ) - .
г , 1 2 :
:
m .x'' = - k . x, x''' + = 0,
m ,
k ,
= k/m .
: E = En + Ek = Enmax = Ekmax
En = k . x2/2 = k . A2 . sin2()/2,
Ek = m . V2/2 = m . A2 . . cos2()/2,
Enmax = k . A2/2, Ekmax = m . A2 . 2/2.
:
= 2 . . ,
= 2 . . ,
ι ,
= 2 . .
I ,
m ,
.
:
m . x'' = - k . x - r . , x'' + 2 . . + = 0,
= r/2m .
г :
x = A(t). cos( t + ),
A(t) = 0. e - ,
0 - t = 0.
= ln = .
A(t) A(t+T) , .
:
m . x'' = - k . x - r . + F0. cos t,
x'' + 2 . . + = f0. cos t,
F0 . cos t , .
= f0/ - ,
= - ,
= f0/(2. . ) .
Q = = /N,
N , .
- (, ).
, .
г :
= A . cos (t - x/V) = A . cos( t - kx),
- x t,
- ,
V ( ),
V = dx/dt = /k,
k = 2 - ,
= V . T - ,
D = 2 .Dx/ - , ( ) D.
|
|
г :
= A . cos( .x/V). cos t = A . coskx. cos t
:
- : V = ,
, - ,
- : V = = ,
- ( = p/v),
R ,
,
- ,
.
: U = d /dk , ,
U = V - . dV/d - ' .
' 㳿:
= . . A2/2,
: ,
j = D/DS | - 㳿,
D = DW/Dt 㳿,
DW ,
DS | - , .
'
1. = 10 . , , xmax = 1 . .
'
г :
x = sin( t + ), (1.13)
,
- ,
t - ,
- .
:
= xmax, (1.14)
= 2 (1.15)
t = 0 (1.13) :
xmax = sin , (1.16)
:
= arcsin(xmax/) = arcsin1,
= (2k + 1) /2, (k = 0,1,2,3...).
2 , , :
= /2. (1.17)
(1.14) - (1.17) :
x = 10-3 sin(20 t + /2), ()
2. V = 20 /. 1 = 12 2 = 15 , = 0,75 . , t = 1,2, = 0,1.
'
, , 2 ; , , , :
= D. / = (2 - 1). / , (1.18)
= (2- 1) / . (1.19)
= (15 - 12)/0,75 = 8.
= /, = /V, :
= 2 V/
= 2 .20/8 = 5 -1
, V, :
y = 0,1 cos5 (t - x/20), () (1.20)
, (1.20) t x:
y1 = 0,1cos5 (1,2 - 12/20) = 0,1cos3 = - 0,1,
y2 = 0,1cos5 (1,2 - 15/20) = 0,1cos2,25 = 0,071.
3. = 4, = 1,6; = 0. t = /4 쳭 = 4,5 . .
'
г :
x = 0 sin( t + ), (1.21)
= 2 / = /2, = 0, = / = 1,6/4 = 0,4 -1.
0 , (1) = 4,5, t = /4 = 1, = 0,4 -1, = /2 = 0.
4,5 = 0 -0,4 sin /2 = 0 -0,4,
0 = 4,5/ -0,4 = 6,7.
(1.21) :
x = 6,7 -0,4t sin t /2 .
4. ҳ 10 . 0 = 7 , = 0, = 1,6 -1. ϳ 䳺 F x = 5 sin(10 t - 3 /4) . .
|
|
'
г :
x = 0 sin t,
- 3 /4,
tg = . /( - ) = tg(- 3 /4) = 1,
= ,
= 10 , = 1,6 -1, = 10,5 .
:
x = 7 -1,6t sin10,5 t, .
г :
F = F0 sin t,
F0 = A.m = 72.10-3 = 72 .
:
F = 72 sin10 t, .