Single Choice

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

A$$\displaystyle \dfrac{\sqrt{3}}{32}\pi^{2}\ \mathrm{c}\mathrm{m}/\mathrm{s}^{2}$$
B$$\displaystyle \dfrac{-\pi^{2}}{32}\ \mathrm{c}\mathrm{m}/\mathrm{s}^{2}$$
C$$\displaystyle \dfrac{\pi^{2}}{32}\ \mathrm{c}\mathrm{m}/\mathrm{s}^{2}$$
D$$-\displaystyle \dfrac{\sqrt{3}}{32}\pi^{2}\ \mathrm{c}\mathrm{m}/\mathrm{s}^{2}$$
Correct Answer

Solution

The given motion is represented by
$$\mathrm{x}=1\sin(\pi/4)\mathrm{t}$$
$$\displaystyle \dfrac{\mathrm{d}^{2}\mathrm{x}}{\mathrm{d}\mathrm{t}^{2}}=\dfrac{-\pi^{2}}{16}\sin(\pi/4)\mathrm{t}$$
At $$\mathrm{t}=4/3\ \mathrm{s}\mathrm{e}\mathrm{c}$$,
$$\displaystyle \frac{\mathrm{d}^{2}\mathrm{x}}{\mathrm{d}\mathrm{t}^{2}}=-\dfrac{\sqrt{3}}{32}\pi^{2}\ \mathrm{c}\mathrm{m}/\mathrm{s}^{2}$$

SIMILAR QUESTIONS

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