First slide

Simple hormonic motion

Question

A particle is executing simple harmonic motion along X-axis with its equilibrium position at the origin. Variation of its velocity with displacement is as shown in the graph. Then maximum acceleration of the particle is

Moderate

A

$10^{3} m / s^{2}$
B

$10^{2} m / s^{2}$
C

$10 m / s^{2}$
D

$1 m / s^{2}$

Solution

From the v-x graph , amplitude A = 0.1m
Maximum velocity $V_{\max} = A ω = 10 m / s \Rightarrow ω = \frac{10}{0 .1} rad / s$
$∴ Maximum accelaration a_{\max} = A ω^{2} = 0 .1 \times {(100)}^{2} m / s^{2} = 10^{3} m / s^{2}$

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