The time period of the variation of potential energy of a particle executing SHM with period T is
Potential energy of particle executing SHM =12mω2x2
The relation between ω and T is given as: T=2πωorω=2πT
Put the value of ω in the potential energy expression as:
U=12m4π2T2x2
=2mπ2x2T2
U∝1T2