First slide

Simple harmonic motion

Question

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

Moderate

A

$25 m / s^{2}$
B

$\frac{4 π^{2}}{5} m / s^{2}$
C

$\frac{2 π^{2}}{5} m / s^{2}$
D

$4 π^{2} m / s^{2}$

Solution

For simple harmonic motion, the acceleration of a particle is given by $a = - A w^{2} \sin (w t)$ . Hence the maximum acceleration of the particle is $a_{\max} = A ω^{2}$ . From the graph, time period of oscillation is 0.2 s. Using the relation $ω = \frac{2 π}{T}$
Hence, $v_{\max} = A ω^{2} = 5 {(\frac{2 π}{5})}^{2} = \frac{4 π^{2}}{5} m s^{- 2}$

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