Q. The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where $E$ is the total energy)
A) $\frac{1}{8}E$
B) $\frac{1}{4}E$
C) $\frac{1}{2}E$
D) $\frac{2}{3}E$
Explanation
(b) $\frac{U}{E} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}} = \frac{\left( \frac{a}{2} \right)^{2}}{a^{2}} = \frac{1}{4} \Rightarrow U = \frac{E}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.