Question 3: Oscillations

Question

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

Accepted Answer

The motion of the particle performing S.H.M. represented by
$$\begin{aligned}
x & =A \sin \omega t=1 \sin \frac{2 \pi}{T} \cdot t=\sin \frac{2 \pi}{8} t \
	herefore \quad x & =\sin \left(\frac{\pi t}{4}ight)
\end{aligned}$$
$$	herefore$$ Velocity, $$v=\frac{d x}{d t}$$
$$=\frac{d}{d t} \sin \left(\frac{\pi}{4}ight) t=\frac{\pi}{4} \cos \left(\frac{\pi}{4}ight) t$$
$$	herefore$$ Acceleration of the particle.
$$\begin{aligned}
a & =\frac{d v}{d t}=\frac{d}{d t}\left[\frac{\pi}{4} \cos \left(\frac{\pi}{4}ight) tight] \
& =-\frac{\pi}{4} \cdot \frac{\pi}{4} \cdot \sin \left(\frac{\pi}{4} tight) \Rightarrow a=-\frac{\pi^2}{16} \sin \left(\frac{\pi}{4} \cdot tight)
\end{aligned}$$
At $$t=2 \mathrm{~s}$$
$$a=-\frac{\pi^2}{16} \cdot \sin \left(\frac{\pi}{4} \cdot 2ight)=-\frac{\pi^2}{16} \mathrm{~ms}^{-2}$$

Answer

$$-\frac{\pi^2}{8} \mathrm{~ms}^{-2}$$

Answer

$$\frac{\pi^2}{16} \mathrm{~ms}^{-2}$$

Answer

$$-\frac{\pi^2}{16} \mathrm{~ms}^{-2}$$

Answer

$$\frac{\pi^2}{8} \mathrm{~ms}^{-2}$$

Oscillations

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

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