Question

For a particle of mass $m$ executing SHM with angular frequency $\omega $ , the kinetic energy $k$ is given by $k=k_{0}cos^{2} \omega t .$ The equation of its displacement can be

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

Answer 1

Answer: (B)

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