Question

For a particle executing SHM, the kinetic energy $K$ is given by $K=K_{0} \cos ^{2} \omega t .$ The equation of its displacement can be

• A. $\left(\frac{K_{0}}{m \omega^{2}}\right)^{1 / 2} \sin \omega t$
• B. $\left(\frac{2 K_{0}}{m \omega^{2}}\right)^{1 / 2} \sin \omega t$
• C. $\left(\frac{2 \omega^{2}}{m K_{0}}\right)^{1 / 2} \sin \omega t$
• D. $\left(\frac{2 K_{0}}{m \omega}\right)^{1 / 2} \sin \omega t$

Answer 1

Answer: (B)

If $m$ is the mass and $r$ is the amplitude of oscillation, then maximum kinetic energy,
or $K_{0} =\frac{1}{2} m \omega^{2} r^{2}$
$ r =\left(\frac{2 K_{0}}{m \omega^{2}}\right)^{1 / 2}$
The displacement equation can be
$y=r \sin \omega t=\left(\frac{2 K_{0}}{m \omega}\right)^{1 / 2} \sin \omega t$