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?

Options

A. `(1)/(12)s`
B. `(1)/(6)s`
C. `(1)/(4)s`
D. `(1)/(3)s`

Answer

B

Explanation

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)ma^(2)omega^(2)cos^(2)omegat=(75)/(100)xx(1)/(2)ma^(2)omega^(2)`
or `cos^(2)omegat=(3)/(4)impliescosomegat=sqrt(3)/(2)=cos.(pi)/(6), therefore omegat=(pi)/(6)`
or `t=(pi)/(6omega)=(pi)/(6(2pi//T))=(2pi)/(6xx2pi)=(1)/(6)s`