First slide

Simple hormonic motion

Question

Which of the following function represents a simple harmonic oscillation

Moderate

A

$\sin ωt - \cos ωt$
B

$\sin^{2} ωt$
C

$\sin ωt + \sin 2 ωt$
D

$\sin ωt - \sin 2 ωt$

Solution

$x = \sin (ω t) - \cos (ω t) = \sqrt{2} \sin (ω t - \frac{π}{4})$ is a SHM with angular frequency $ω$ .
$x = \sin^{2} (ω t) = \frac{1}{2} - \frac{1}{2} \cos (2 ω t)$ is a SHM about equilibrium position $x = \frac{1}{2}$ with angular frequency $2 ω$ .
The last two equations do not represent SHM because multiple frequencies are present in each case.

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