Q. A particle is oscillating in SHM. What fraction of total energy is kinetic when the particle is at $\frac{A}{2}$ from the mean position? ($A$ is the amplitude of oscillation)
A) $\frac{3E}{2}$
B) $\frac{3}{4}\ E$
C) $\frac{E}{2}$
D) $3E$
Explanation
(b) Kinetic energy in SHM
$KE = \frac{1}{2}m\omega^{2}(A^{2} - x^{2})$
At $x = \frac{A}{2}$
$KE = \frac{1}{2}m\omega^{2}\left( A^{2} - \frac{A^{2}}{4} \right) = \frac{3}{4}(\frac{1}{2}m\omega^{2}A^{2})$
$= \ \frac{3}{4} \times$ Total energy of the particle
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.