For a particle executing S.H.M. the displacement x is given by $\mathrm{x}=\mathrm{Acos\omega t}$. Identify the graph which represents the variation of potential energy (P.E.) as a function of time t and displacement x 

Potential energy is minimum (in this case zero) at mean position (x = 0) and maximum at extreme position $(\mathrm{x}=\pm \mathrm{A}).$

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.