Question

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

• A. $\frac{\sqrt{3}}{32}{\pi }^{2}cm/s^2$
• B. $\frac{-{\pi }^2}{32}cm/s^2$
• C. $\frac{{\pi }^2}{32}cm/s^2$
• D. $-\frac{\sqrt{3}}{32}{\pi }^{2}cm/s^2$

Answer 1

The correct option is D $-\frac{\sqrt{3}}{32}{\pi }^{2}cm/s^2$

The given motion is represented by
$x=1\sin \left(\pi /4\right)t$
$\frac{d^{2}x}{d{t}^2}=\frac{-{\pi }^2}{16}\sin \left(\pi /4\right)t$
At $t=4/3sec$,
$\frac{d^{2}x}{d{t}^2}=-\frac{\sqrt{3}}{32}{\pi }^{2}cm/s^2$