When the displacement is half the amplitude, the ratio of po... | PHYSICS - ENERGY IN SIMPLE HARMONIC MOTION | SolveeIt | Solveeit

Today, August 19

Question

When the displacement is half the amplitude, the ratio of potential energy to the total energy is

A

$\frac{1}{2}$

B

$\frac{1}{4}$

C

$1$

D

$\frac{1}{8}$

Answer

$\frac{1}{4}$

Explanation

Solution

$\frac{U}{E} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}} = \frac{\left( \frac{a}{2} \right)^{2}}{a} = \frac{1}{4}$