Explanation

(b) Here, $y = \sin^{2}{\omega t}$
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$\frac{dy}{dt} = 2\omega\sin{\omega t\cos{\omega t}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \omega\sin{2\omega t}$
$\frac{d^{2}y}{dt^{2}} = 2\omega^{2}\cos{2\omega t}$
For SHM, $\frac{d^{2}y}{dt^{2}} \propto - y$
Hence, function is not SHM, but periodic.
From the $y$-$t$ graph, time period is
$T = \frac{\pi}{\omega}$