The kinetic energy, $K$ of a body performing simple harmonic motion varies with time $t$, is indicated in graph

Kine tic energy of a body performing simple harmonic motion is given as $$ K=\frac{1}{2} m v^2 $$ where, $$ \begin{aligned} & v=\frac{d y}{d t}=\frac{d}{d t} \cdot a \sin \omega t \quad[\because y=a \sin \omega t] \\ & v=a \omega \cos \omega t \end{aligned} $$ $\therefore$ From Eq. (i), we get $$ \begin{aligned} & K=\frac{1}{2} m(a \omega \cos \omega t)^2=\frac{1}{2} m a^2 \omega^2 \cos ^2 \omega t \\ & K=\frac{1}{2} m a^2 \omega^2\left(\frac{1+\cos 2 \omega t}{2}\right) \quad \ldots(\text { i }) \end{aligned} $$ The graph represented in option (1) is correct for expression of kinetic energy represented by Eq. (i).