Q. The function $\sin^{2}{(\omega t)}$ represents
A) A periodic, but not simple harmonic motion with a period $2\pi/\omega$
B) A periodic, but not simple harmonic motion with a period $\pi/\omega$
C) A simple harmonic motion with a period $2\pi/\omega$
D) A simple harmonic motion with a period $\pi/\omega$
Explanation
(b) Here, $y = \sin^{2}{\omega t}$
$\frac{dy}{dt} = 2\omega\sin{\omega t\cos{\omega t = \omega\sin{2\omega t}}}$
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$\frac{d^{2}y}{dt^{2}} = 2\omega^{2}\cos{2\omega t}$
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
$t = \frac{\pi}{\omega}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.