The function $sin^2\,(\omega t)$ represents
AIIMS 2008, Medium
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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 $SHM.$
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