First slide

Simple harmonic motion

Question

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

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{4}$
C

1
D

$\frac{1}{8}$

Solution

$\frac{U}{E} = \frac{\frac{1}{2} {mω}^{2} y^{2}}{\frac{1}{2} {mω}^{2} a^{2}} = \frac{y^{2}}{a^{2}} = \frac{{(\frac{a}{2})}^{2}}{a} = \frac{1}{4}$

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