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

Answer

A

Explanation

K.E. of a body undergoing SHM is given by,
`K.E.=(1)/(2)ma^(2)omega^(2)cos^(2)omega t` and `T.E.=(1)/(2)ma^(2)omega^(2)`
Given `K.E.=0.75T.E.implies0.75=cos^(2)omega timpliesomega t=(pi)/(6)`
`implies" "t=(pi)/(6xxomega)impliest=(pixx2)/(6xx2pi)impliest=(1)/(6)s`