A particle executes simple harmonic motion with a frequency, $f$. The frequency with which its kinetic energy oscillates is

Let $X=Asin\omega t$

$V=\frac{dx}{dt}=A\omega cos\omega t$

$K=\frac{1}{2}m{V}^2=\frac{1}{2}m{\omega }^2{A}^{2}co{s}^2\left(\omega t\right)$

$K=\frac{1}{2}m{\omega }^2{A}^2\left(\frac{1+cos2\omega t}{2}\right)$

$K=\frac{1}{4}m{\omega }^2{A}^2(1+cos2\omega t)$

${\omega }_k=2\omega$

Hence the frequency of oscillation of kinetic energy is 2f