Periodic with time period but not simple harmonic motion (SHM)

Question

Match List-I with List-II. [2026]

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

Choose the correct answer from the options given below.

Smart Achievers · Accepted Answer

(1)

$(A)$ $\sin^{2} ω t = \frac{1}{2} - \frac{1}{2} \cos 2 ω t, it represents SHM motion having$ $period T = \frac{π}{ω}$

$(B)$ $\sin^{3} 2 ω t = \frac{3}{4} \sin 2 ω t - \frac{1}{4} \sin 6 ω t, the common period \frac{π}{ω} but not SHM.$

$(C)$ $\sin ω t + \cos π ω t \to no common period hence it is a nonperiodic function$

$\cos ω t + \cos 2 ω t$ $\cos ω t + \cos 2 ω t common period \frac{2 π}{ω} but it do not represent SHM.$

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