6 8 - § . M oddiy nuqtaning s o ‘nuvchi tebranma harakati M assasi m b o ‘lgan M m oddiy nuqta qaytaruvchi kuch va m u h it-
ning qarshilik kuchi ta ’sirida to ‘g‘ri chiziqli harakatda bo‘lsin (133-rasm).
M u h itn in g q arsh ilik k u c h in i m o d d iy n u q ta tezligining b irin c h i
darajasiga p rop orsion al deylik:
R = - ц х .
(68.1)
M У ~ - Bu h arakatn i tekshirish u ch u n m od-
0 ,— £—
^ * У ___ x diy nuq ta harakatining differensial teng-
- x --------------
133-rasm. - r
lam asini tuzam iz:
mx = —cx — \ix . (
68.2)
(
68.2) ni quyidagi ko‘rinishda yozamiz:
m x + цх + cx = 0 .
(68.3)
(68.3) ning ikki to m o n in i m ga b o ‘lib, — = k 2 , — = 2bdeb bel-
m m gilaym iz. N atijada
x + 2bx + k 2x = Q (68.4)
kelib chiqadi.
B oshlang‘ich p a y td a M n u q ta MQ d a b o ‘lib, u n in g absissasi x0,
tezligi V0 b o ‘lsin. (68.4) ning yechim ini to p ish uch u n xarakteristik
te n g la m a tuzam iz:
n2 +
2 bn + k 2 = 0 .
Bu ten g lam a y echim i
щ 2 - ~ b ± y/b2 - к 2 k o ‘rin ish d a b o £lib, u n d a g i b va к ga n isb a ta n quyidagi h o lla r u c h -
rashi m um kin:
1) к > b — q arsh ilik kuchi qaytaruvchi kuchga nisbatan kichik
boMgan hoi;
2) к < b — q a rsh ilik k u c h i qay taru v ch i k u ch g a n isb atan k a tta
boMgan hoi;
3) к = b — c h e g a ra hoi.
118
Bu ho llarni alo h id a-alo h id a tekshiram iz.
1)
