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

A

Explanation

As the body starts from the origin, so
`x=Asinomegat therefore v=(dx)/(dt)=Aomegacosomegat`
Kinetic energy, `K=(1)/(2)mv^(2)=(1)/(2)m(Aomegacosomegat)^(2)`
Total energy, `E=(1)/(2)mA^(2)omega^(2)`
As `K=75%" of "E=(75)/(100)E`
`therefore (1)/(2)mA^(2)omega^(2)cos^(2)omegat=(75)/(100)((1)/(2)mA^(2)omega^(2))`
or `cos^(2)omegat=(3)/(4)orcosomegat=(sqrt(3))/(2)=cos.(pi)/(6) therefore omegat=(pi)/(6)`
or `t=(pi)/(6omega)=(pi)/(6(2pi//T))=(2pi)/(6xx2pi)=(1)/(6)s`