First slide

Simple hormonic motion

Question

The function $\sin^{2} (ωt)$ represents:

Moderate

A

a simple harmonic motion with a period $\frac{2 π}{ω}$
B

a simple harmonic motion with a period $\frac{π}{ω}$
C

$a periodic, but not simple harmonic motion with a period \frac{2 π}{ω}$
D

a periodic, but not simple harmonic motion with a period $\frac{π}{ω}$

Solution

$x = \sin^{2} (ω t) = \frac{1}{2} - \frac{1}{2} \cos (2 ω t)$ which is a SHM of angular frequency $2 ω$ about the equlibrium position $x = \frac{1}{2}$ .
Period, T = $\frac{2 π}{2 ω} = \frac{π}{ω}$

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