Question

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

• A. $f/2$
• B. $f$
• C. $2f$
• D. $4f$

Answer 1

Answer: (C)

For a particle executing SHM the displacement equation is given by
$y=a\sin \omega t=a\sin 2\pi ft.$
kinetic energy $KE=\frac{1}{2}m{v}^2$
$=\frac{1}{2}m{\left(\frac{dy}{dt}\right)}^2$
where $\frac{dy}{dt}=2\pi fa\cos 2\pi ft$
$\therefore KE=\frac{1}{2}m\{(2\pi fa{)}^2{\cos }^{2}2\pi ft\}$
$KE\propto (1+\cos 4\pi ft)$
$\cos 4\pi ft$ changes periodically with frequency $2f.$