First slide

Simple harmonic motion

Question

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is

Moderate

A

$a / 4$
B

$a / 3$
C

$a / 2$
D

$2 a / 3$

Solution

$\frac{U}{U_{\max}} = \frac{\frac{1}{2} {mω}^{2} y^{2}}{\frac{1}{2} {mω}^{2} a^{2}}$ $\Rightarrow \frac{1}{4} = \frac{y^{2}}{a^{2}}$ $\Rightarrow y = \frac{a}{2}$

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