First slide

Simple hormonic motion

Question

The x-t graph of a particle undergoing simple harmonic motion is shown in the Fig. The acceleration of the particle at $t = \frac{4}{3} \sec$ is :

Easy

A

$\frac{\sqrt{3}}{32} π^{2} cm / s^{2}$
B

$\frac{- π^{2}}{32} cm / s^{2}$
C

$\frac{π^{2}}{32} cm / s^{2}$
D

$\frac{- \sqrt{3} π^{2}}{32} cm / s^{2}$

Solution

$x = \sin (\frac{2 π}{8} t) \Rightarrow a = - ω^{2} x = - {(\frac{2 π}{8})}^{2} \times \sin (\frac{2 π}{8} \times \frac{4}{3}) = - \frac{π^{2}}{16} \times \frac{\sqrt{3}}{2} = \frac{- \sqrt{3} π^{2}}{32} cm / s^{2}$

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