The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t=2 s$ is :
NEET 2023, Medium
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$x = A \sin (\omega t )$
$\frac{ dx }{ dt }= v = A \omega \cos (\omega t )$
$\frac{ dv }{ dt }= a =-\omega^2 A \sin (\omega t )$
$a =-\left(\frac{2 \pi}{8}\right)^2 \times 1 \sin \left(\frac{2 \pi}{8} \times 2\right)$
$\Rightarrow a =-\frac{\pi^2}{16} \times \sin \left(\frac{\pi}{2}\right)$
$\therefore a =\frac{-\pi^2}{16}\,m / s ^2$
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