A particle moves on the X-axis according to the equation `x=x_0 sin^2omegat`. The motion simple harmonic

Options

A. with amplitude `x_0`
B. with amplitude `2x_0`
C. with time period `2pi//omega`
D. with time period `pi//omega`

Answer

D

Explanation

`x=x_0sin^2omegat=x_0/2(2sin^2omegat)`
`=x_0/2(1-cos2omegat)`
`x=x_0/2-x_0/2cos2omegat`
`x=B-Acosomega^'t`
Amplitude `=x_0/2`, `omega^'=2omega`
`T^'=(2pi)/(omega)=(2pi)/(omega)=pi/omega`