First slide

Simple hormonic motion

Question

A particle is vibrating simple harmonically with an amplitude 'a' . Tlte displacement of the particle when its energy is half kinetic and half potential is

Moderate

A

$\frac{a}{2}$
B

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

$\frac{a}{4}$
D

zero

Solution

Kinetic energy = Potential energy
$\frac{1}{2} {mω}^{2} (a^{2} - y^{2}) = \frac{1}{2} {mω}^{2} y^{2}$
$a^{2} - y^{2} = y^{2}$
$2 y^{2} = a^{2} \Rightarrow y = \pm \frac{a}{\sqrt{2}}$

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