B oshlang‘ich paytda
M n u q ta
M 0 da b o i ib ,
uning k oo rd in atasi
x0, tezligi
V0 b o ‘lsin.
M oddiy nuqtan in g harak at differensial ten g lam asin i tuzam iz:
mx = - c x + Q0 sin (p t + 5 ) .
(69.2)
(69.2) ni quyidagi k o ‘rin ish d a yozib olam iz:
mx + cx =
Qo sin (p t + 8 ).
2
с
Q
к = —,
P0 = — belgilashlar kiritsak:
x + k 2x = P0 sin(
p t +
8 )
(69.3)
hosil b o ‘ladi.
D ifferensial tenglam alar nazariyasidan m a ’lum ki, (69.3) differen-
sial ten g lam a yechim i quyidagicha yoziladi:
x = x, +
x2 .
(69.4)
(69.4) da X,
bilan bir jinsli
x +
k 2x = 0
(69.5)
differensial tenglam aning um um iy yechim i belgilangan; x
2 esa (69.3)
ning xususiy yechim idan iborat.
(69.5) differensial ten glam an in g um um iy yechim i:
x, = o s in ( £ / + a )
(69.6)
k o ‘rinish d a ifodalanishi bizga m a ’lum.
(69.3) o'zgarm as koeffitsiyentli chiziqli bir jinsli differensial ten g
lam aning xususiy yechim ini quyidagi ko‘rinishda olam iz:
x
2 =
B s \n (p t + 5 ).
(69.7)
(69.7) dagi
В koeffitsiyentni aniqlash u ch u n (69.7) dan vaqt b o ‘-
yicha ikkinchi tartibli hosila olam iz:
x
2 =
- B p 2 sin (/tf + 8) .
(69.8)
(69.7) va (69.8) ni (69.3) ga
q o ‘y a m i z :
