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

Show that y=sin^(2)omegat does not represent simple harmonic but perio

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