For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$
IIT 2003, Medium
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(a) 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.
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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