Q. The kinetic energy and the potential energy of a particle executing S.H.M. are equal. The ratio of its displacement and amplitude will be
A) $\frac{1}{\sqrt{2}}$
B) $\frac{\sqrt{3}}{2}$
C) $\frac{1}{2}$
D) $\sqrt{2}$
Explanation
(a) Given$\ K.E.\ = P.E. \Rightarrow \frac{1}{2}mv^{2} = \frac{1}{2}kx^{2}$
$\Rightarrow \frac{1}{2}m\omega^{2}\left( a^{2} - x^{2} \right) = \frac{1}{2}m\omega^{2}x^{2}$
$\Rightarrow a^{2} - x^{2} = x^{2} \Rightarrow x^{2} = \frac{a^{2}}{2} \Rightarrow \frac{x}{a} = \frac{1}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.