Question

When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is $n$, the frequency of the kinetic energy is:

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

Answer 1

The correct option is C $2n$

Let displacement of particle of mass $m$, $x=A\sin \omega t$

$\omega$=angular frequency of oscillation

frequency, $f=\frac{\omega }{2\pi }$

velocity $v=\frac{dx}{dt}$

$=\omega A\cos \omega t$

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

$=\frac{1}{4}m{\omega }^2{A}^2(1+\cos \left(2\omega t\right))$

Now for kinetic energy the cosine part determine frequency which is

$f^{\prime }.\frac{2\omega }{2\pi }.\frac{\omega }{\pi }-2\omega$

$\Rightarrow f^{\prime }.2f$