Show that `y=sin^(2)omegat` does not represent simple harmonic but periodic. What is the period of the given function.

Explanation

Given, `y=sin^(2)omegat` or `y=(1)/(2)(1-cos 2omegat)`
Velocity of the particle `v=(dy)/(dx)=(1)/(2)[0+(sin2omegat)(2omega)]`
`v=(omega)sin2omegat`
Particle acceleration `a=(dv)/(dt)=2omega^(2)cos2omega t`
Hence `y=sin^(2)omegat` is periodic but does not execute S.H.M. Acceleration is not proportional to the displacement.