First slide

Oscillation motion

Question

Which of the following expression does not represent SHM?

Moderate

A

$A \cos ωt$
B

$A sin 2 ωt$
C

$A \sin ωt + B \cos ωt$
D

$A \sin^{2} ωt$

Solution

For SHM, $\frac{d^{2} y}{{dt}^{2}} \propto - y$
If $y = A \sin^{2} ωt$
$\frac{dy}{dt} = (2 A \sin ωt \cos ωt) ω$
= $= Aω \sin 2 ωt$
$\frac{d^{2} y}{{dt}^{2}} = + 2 {Aω}^{2} \cos 2 ωt$
i.e., $\frac{d^{2} y}{{dt}^{2}} is not proportional to - y$

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