The function sin ²(ω t) represents (a) a periodic, but not SHM with a period (π)/(ω) (b) a periodic, but not SHM with a period (2π)/(ω) (c) a SHM with a period (π)/(ω) (d) a SHM with a period (2π)/(ω)

Answer: (a). sin ²ω t = 1/2 - 1/2cos 2ω t It repeats when 2ω t changes by 2π, so period T = (π)/(ω). Displacement from the origin does not satisfy (d²y)/(dt²) = -ω'² y (it has a constant term), so it is periodic but not SHM. So the answer is (a).

The function sin ²(ω t) represents | JEE Main 2005 (AIEEE)

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Periodic Motion & SHM Basics

The function $\sin^2(\omega t)$ represents

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Answer: (a)

$\sin^2\omega t = \frac{1}{2} - \frac{1}{2}\cos 2\omega t$
It repeats when $2\omega t$ changes by $2\pi$ , so period $T = \frac{\pi}{\omega}$ .
Displacement from the origin does not satisfy $\frac{d^2y}{dt^2} = -\omega'^2 y$ (it has a constant term), so it is periodic but not SHM.
So the answer is (a).

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