First slide

Simple harmonic motion

Question

The kinetic energy of a particle executing S.H.M. is 16 J when it is at its mean position. If the mass of the particle is 0.32 kg, then what is the maximum velocity of the particle

Easy

A

$5 m / s$
B

$15 m / s$
C

$10 m / s$
D

$20 m / s$

Solution

Kinetic energy at mean position,
$K_{\max} = \frac{1}{2} {mv}_{\max}^{2} .$ $\Rightarrow v_{\max} = \sqrt{\frac{2 K_{\max}}{m}}$
$= \sqrt{\frac{2 \times 16}{0 .32}}$ $= \sqrt{100}$ $= 10 m / s .$

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