Question

An 8kg body performs SHM of amplitude 30cm. The restoring fore is 60n, when the displacement is 30cm. Find (a) time period (b) the acceleration, P.E and K.E., when displacement is 12 cm.

Answer 1

Here, `m=8kg,`
`a=30cm=0.30m,`
(a) `F=60N, y=0.30m`
`F=ky or k=(F)/(y)=(60)/(0.30)=200Nm^(-1)`
`omega=sqrt((k)/(m))=sqrt((200)/(8))=5rad//s^(-1)`
Time period, `T=(2pi)/(omega)=(2xx22)/(7xx5)=(44)/(35)=1.256s`
(ii) Here, `y=12cm=0.12m.`
`:.` Acceleration, `A=omega^(2)y=(5)^(2)xx0.12`
`=3.0ms^(-2)`
P.E. `=(1)/(2)KY^(2)=(1)/(2)xx(200)xx(0.12)^(2)=1.44J`
K.E. `(1)/(2)k(a^(2)-y^(2))`
`=(1)/(2)xx200xx[(0.30)^(2)-(0.12)^(2)]=7.56J`