First slide

Simple hormonic motion

Question

For a particle executing S.H.M. the displacement x is given by x = A cos $ωt$ . Identify the graph which represents the variation of potential energy (P.E.) as a function of time t and displacement x

Easy

A

I, III
B

II, IV
C

II, III
D

I, IV

Solution

Potential energy is minimum (in this case zero) at mean position (x = 0) and maximum at extreme position (x = $\pm$ A).
At time t = 0, x = A, hence potential should be maximum. Therefore graph I is correct.
Further in graph III, potential energy is minimum at x = 0, hence this is also correct.

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