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Q.

The x-t graph of a particle undergoing simple harmonic motion with amplitude 1cm is shown below. The acceleration of the particle at t = 4/3 sec. is

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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

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

answer is D.

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Detailed Solution

$\begin{array}{l} T = 8 \sec; A = 1 cm \\ a = - ω^{2} Asin ωt = - {(\frac{2 π}{8})}^{2} \times 1 \times \sin (\frac{2 π}{8} \times \frac{4}{3}) \\ = - \frac{4 π^{2}}{64} \times \sin 60^{0} = - \frac{4 π^{2}}{64} \times \frac{\sqrt{3}}{2} = - \frac{\sqrt{3}}{32} π^{2} {cms}^{- 2} \end{array}$

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The x-t graph of a particle undergoing simple harmonic motion with amplitude 1cm is shown below. The acceleration of the particle at t = 4/3 sec. is