Question

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 $\text{(P.E.)}$ as a function of time $t$ and displacement $x$.

• A. $\text{I, III}$
• B. $\text{II, IV}$
• C. $\text{II, III}$
• D. $\text{I, IV}$

Answer 1

The correct option is A $\text{I, III}$

We know, potential energy is minimum 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 $\text{I}$ is correct.
Further in graph $\text{III}$, potential energy is minimum at $x=0$, hence this is also correct.