First slide

Simple hormonic motion

Question

For a particle executing SHM the displacement x is given by x = Acos $ω$ t. Identify the graph which represents the variation of potential energy (PE) as a function of time t and displacement x -

Moderate

A

I and III
B

II and IV
C

II and III
D

I and IV

Solution

$PE = \frac{1}{2} {mω}^{2} A^{2} \cos^{2} ωt at t = 0, PE i s m a x i m u m and at t = \frac{T}{4}, ωt = \frac{π}{2} . Hence graph I r e p r e s e n t s P E . PE = \frac{1}{2} {mω}^{2} x^{2} at x = 0, PE = 0 at x = \pm A, PE = max . Graph III .$

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