Which functions of time are SHM, and their period

This type of question, asked 2 times: 2021 Paper 10, 5 Apr 2026 S2. All 2 questions below, oldest first.

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Question 1
2021 Paper 10
14 $\frac{\pi}{\omega}$
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Question 2

5 Apr 2026 S2

\sin^{2}\omega t

List-I	List-II
(A) $\sin^{2}\omega t$	(I) Periodic with time period $T = \frac{\pi}{\omega}$ but not simple harmonic motion (SHM)
(B) $\sin^{3}(2\omega t)$	(II) Periodic with time period $T = \frac{2\pi}{\omega}$ but not SHM
(C) $\sin(\omega t) + \cos(\pi\omega t)$	(III) Periodic with time period $T = \frac{\pi}{\omega}$ and SHM
(D) $\cos\omega t + \cos 2\omega t$	(IV) Non-periodic

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