First slide

Simple hormonic motion

Question

The displacement of a particle along the x-axis is given by $x = a \sin^{2} ωt$ . The motion of the particle corresponds to

Difficult

A

simple harmonic motion of frequency $\frac{ω}{π}$ with position of equilibrium position shifted to x= a/2 .
B

simple harmonic motion of frequency $\frac{3 ω}{2 π}$
C

nonsimple harmonic motion
D

simple harmonic motion of frequency $\frac{ω}{2 π}$

Solution

$T h e g i v e n e q u a t i o n x = a \sin^{2} ω t = \frac{a}{2} \times 2 \sin^{2} ω t = \frac{a}{2} - \frac{a}{2} \sin 2 ω t . T h e a b o v e e q u a t i o n r e p r e s e n t s S H M w i t h p o s i t i o n o f e q u i l i b r i u m a t x = a / 2 .$

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