First slide

Simple harmonic motion

Question

A particle executing simple harmonic motion with amplitude of 0.1 m. At a certain instant when its displacement is 0.02 m, its acceleration is 0.5 m/s². The maximum velocity of the particle is (in m/s)

Moderate

A

0.01
B

0.05
C

0.5
D

0.25

Solution

Acceleration $A = ω^{2} y$ $\Rightarrow ω = \sqrt{\frac{A}{y}} = \sqrt{\frac{0 .5}{0 .02}} = 5$
Maximum velocity $v_{\max} = aω = 0 .1 \times 5 = 0 .5$

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