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The $x - t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t = 4 / 3 s$ is

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$\frac{π^{2}}{32} cm s^{- 2}$

$\frac{\sqrt{3}}{32} π^{2} {cms}^{- 2}$

$- \frac{\sqrt{3}}{32} π^{2} {cms}^{- 2}$

$\frac{- π^{2}}{32} {cms}^{- 2}$

answer is B.

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Detailed Solution

$T = 8 s, ω = \frac{2 π}{T} = (\frac{π}{4}) {rads}^{- 1} x = A \sin ωt;$

$t = \frac{4}{3} S, a = - ω^{2} x$

$a = - (\frac{\sqrt{3}}{32} π^{2}) {cms}^{- 2}$

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