Question 311: Oscillations

Question

A simple pendulum performs simple harmonic motion about $$\mathrm{x}=0$$ with an amplitude '$$\mathrm{a}$$' and time period '$$T$$'. The speed of the pendulum at $$x=\frac{a}{2}$$ is

Accepted Answer

$$\begin{aligned}
\mathrm{v} & =\omega \sqrt{\mathrm{a}^2-\mathrm{x}^2} \
& 	ext { At } \mathrm{x}=\frac{\mathrm{a}}{2}, \
	herefore \quad \mathrm{v} & =\omega \sqrt{\mathrm{a}^2-\frac{\mathrm{a}^2}{4}} \
& =\omega \frac{\sqrt{3 \mathrm{a}}}{2} \
& =\frac{2 \pi}{\mathrm{T}} 	imes \frac{\sqrt{3} \mathrm{a}}{2} \quad .....\left(\because \omega=\frac{2\pi}{T}ight)\
	herefore \quad \mathrm{v} & =\frac{\pi \mathrm{a} \sqrt{3}}{\mathrm{~T}}
\end{aligned}$$

Answer

$$\frac{\pi \mathrm{a}}{\mathrm{T}}$$

Answer

$$\frac{3 \pi^2 \mathrm{a}}{\mathrm{T}}$$

Answer

$$\frac{\pi \mathrm{a} \sqrt{3}}{\mathrm{~T}}$$

Answer

$$\frac{\pi \mathrm{a} \sqrt{3}}{2}$$

Oscillations

A simple pendulum performs simple harmonic motion about $\mathrm{x}=0 with an amplitude '\mathrm{a}' and time period 'T'. The speed of the pendulum at x=\frac{a}{2}$ is

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