JEE Main · 2017 · 02 Apr 2017 · Offline · Elasticity & SHM

Starting from equilibrium the displacement is $x=A\sin \omega t$, so the speed is $A\omega \cos \omega t$ and the kinetic energy $\frac{1}{2}m{A}^2{\omega }^2{\cos }^2\omega t$. Writing ${\cos }^2\omega t=\frac{1}{2}(1+\cos 2\omega t)$ shows the kinetic energy starts at its maximum at $t=0$ and oscillates with half the period, $\frac{T}{2}$. The curve that begins at its peak and repeats every $\frac{T}{2}$ is the right one.