Starting from the origin a body executes simple harmonic oscillation with the period 2s. The time after which its potential energy will be `25%` of the total energy is :

Options

A. `(pi)/(omega)`
B. `(pi)/(6omega)`
C. `(pi)/(3omega)`
D. `(pi)/(9omega)`

Answer

B

Explanation

P.E. `((25)/(100))` of total energy
`=(1)/(4)E=(1)/(4)xx(1)/(2)m omega^(2)a^(2)`
`P.E. =(1)/(2) m omega^(2)a^(2) sin^(2) omegat`
`=(1)/(4)xx(1)/(2) m omega^(2)a^(2)`
`:.sin^(2)omega t=(1)/(4)`
`:. Sin omega=(1)/(2) rArr "sin" (pi)/(6)`
`:.omegat=(pi)/(6)`
`:.t=(pi)/(6omega)`