First slide

Simple harmonic motion

Question

The displacement time graph of an oscillating particle. Find the maximum velocity of the particle.

Moderate

A

2 m/s
B

$π$ m/s
C

2 $π$ m/s
D

$\frac{π}{2}$ m/s

Solution

For simple harmonic motion, the velocity of a particle is given by $v = A w \cos (w t)$ . Hence the maximum velocity of the particle is $v_{\max} = A ω$ . From the graph, time period of oscillation is 0.2 s. Using the relation $ω = \frac{2 π}{T}$
Hence, $v_{\max} = A ω = 0.2 (\frac{2 π}{0.2}) = 2 π m s^{- 1}$

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