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Velocity & Acceleration in SHM question from NEET 2023

Q45NEET 2023Medium

Velocity & Acceleration in SHM

The $x\text{-}t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t = 2\text{ s}$ is:

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Answer: (c)

From the graph: $A = 1$ m, $T = 8$ s, so $\omega = \frac{2\pi}{8} = \frac{\pi}{4}$ rad/s.
At $t = 2$ s the particle is at the extreme, $x = +1$ m.
$a = -\omega^2 x = -\frac{\pi^2}{16}\times 1$ .
So the answer is (c) $-\frac{\pi^2}{16}$ m s $^{-2}$ .

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