a
Clearly \(\sin ^{2} \omega t\) is a periodic function as \(sin\, \omega t\) is periodic with period \(\pi / \omega\)

For \(SHM\) \(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dt}^{2}} \propto-\mathrm{y}\)

\(\frac{\mathrm{dy}}{\mathrm{dt}}=2 \omega \sin \omega t \cos \omega t=\omega \sin 2 \omega t\)

\(\frac{d^{2} y}{d t^{2}}=2 \omega^{2} \cos 2 \omega t\) which is not proporti-

onal \(to - y.\) Hence it is not in \(SHM.\)