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. (a) `1/6s`
B. (b) `1/4s`
C. (c )`1/3s`
D. (d) `1/(12)s`

Answer

A

Explanation

(a) K.E of a body undergoing SHM is given by,
K.E.=1/2ma^(2)omega^(2) cos^(2) omegat, T.E.=1/2ma^(2)omega^(2)`
Given K.E.=0.75T.E`.
`rArr0.75=cos^(2)omegat rArromegat=(pi)/6`
`rArrt=(pi)/(6xxomega)rArr t=(pixx2)/(6xx2pi)rArr t=1/6s`