When a particle executing SHM oscillates with a frequency v, then the kinetic energy of the particle

We know that, kinetic energy, $\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2$

where, $\mathrm{v}=\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{\omega A} \cos \mathrm{\omega t}$

So,      $\mathrm{K}=\frac{1}{2}{\mathrm{m\omega }}^2{\mathrm{A}}^2 {\cos }^2 \mathrm{\omega t}$

Hence, kinetic energy varies periodically with double the frequency of SHM. So, when a particle executing SHM 
oscillates with a frequency v, then the kinetic energy of particle changes periodically with a frequency of 2v.