First slide

Simple harmonic motion

Question

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude = a) is

Moderate

A

$\frac{a}{2}$
B

$a \sqrt{2}$
C

$\frac{a}{\sqrt{2}}$
D

$\frac{a \sqrt{2}}{3}$

Solution

Suppose at displacement y from mean position potential energy = kinetic energy
$\Rightarrow \frac{1}{2} m (a^{2} - y^{2}) ω^{2} = \frac{1}{2} {mω}^{2} y^{2}$
$\Rightarrow a^{2} = 2 y^{2}$ $\Rightarrow y = \frac{a}{\sqrt{2}}$

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