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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=8 / 3 <img alt="" src="https://cdn.entrance360.com/media/up

The  x-t graph of a Particle undergoing simple harmonic motion is shown below. The acceleration of the Particle at  t=8 / 3



 

Option: 1

-\frac{\sqrt{7} \pi^2}{128} \mathrm{~cm} / \mathrm{s}^2


Option: 2

-\frac{\sqrt{5} \pi^2}{128} \mathrm{~cm} / \mathrm{s}^2


Option: 3

-\frac{\sqrt{2} \pi^2}{128} \mathrm{~cm} / \mathrm{s}^2


Option: 4

-\frac{\sqrt{3} \pi^2}{128} \mathrm{~cm} / \mathrm{s}^2


Answers (1)

best_answer

x =A \sin \omega t \\

x =A \sin \frac{2 \pi}{T} \cdot t \\

x =1 \cdot \sin \frac{2 \pi}{16} t \\

x =\sin \frac{\pi}{8} t \\

a =\frac{d^2 x}{dt^2}=-\left(\frac{\pi}{8}\right)^2 \sin \left(\frac{\pi}{8} \cdot t\right) \\

=-\frac{\pi^2}{64} \times \sin \frac{\pi}{8} \times \frac{8}{3} \\

-\frac{\pi^2}{64} \sin \frac{\pi}{3} \\

\frac{-\pi^2}{64} \times \frac{\sqrt{3}}{2}=-\frac{\sqrt{3} \pi^2}{128} \mathrm{~cm} / \mathrm{s}^2
 

Posted by

SANGALDEEP SINGH

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