First slide

Simple hormonic motion

Question

A particle is executing simple harmonic motion with an amplitudes a. When its kinetic energy is equal to its potential energy, its distance from the mean position is

Easy

A

$a / 2$
B

$a / \sqrt{2}$
C

$a / \sqrt{3}$
D

$a / 3$

Solution

$\frac{1}{2} {mω}^{2} (a^{2} - y^{2}) = \frac{1}{2} {mω}^{2} y^{2} 2 y^{2} = a^{2} or y^{2} = \frac{a^{2}}{2} or y = \frac{a}{\sqrt{2}}$

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