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Starting from the origin a body osillate...

Starting from the origin a body osillates simple harmonicall with a period of 2 s. A fter what time will its kinetic energy be 75% of the total energy?

A

`1/6s`

B

`1/4s`

C

`1/3s`

D

`1/12s`

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of SHM will be `x=a sinomegat` during simple harmonic motion,
kinetic energy =`(1)/(2)mv^(2)=(1)/(2)m(aomegacosomegat)^(2)`
Total energy `E=(1)/(2)ma^(2)omega^(2)` because (Kinetic energy)=`(75)/(100)(E)`
or `1/2 m A^(2) omega^(2) cos^(2) omega t = 75/100 xx1/2m a^(2) omega^(2)`
` cos^(2) omega t=3/4 impliescos omega t=sqrt(3)/2 = cospi/5` therefore `omega t=pi/6`
or `t= pi/(6omega) = pi/(6(2pi//T)) = pi/(6^xxpi) = 1/6 sec`.
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