Question 331: Oscillations

Question

A bob of simple pendulum of mass 'm' perform $$\mathrm{SHM}$$ with amplitude '$$\mathrm{A}$$' and period 'T'. Kinetic energy of pendulum of displacement $$x=\frac{A}{2}$$ will be

Accepted Answer

$$\begin{aligned}
& 	ext { Kinetic energy }=\frac{1}{2} m \omega^2\left(A^2-x^2ight) \
& 	ext { At } x=\frac{A}{2}, 	ext { K.E. }=\frac{1}{2} m \omega^2\left(\frac{3}{4} A^2ight)=\frac{3}{8} m \omega^2 A^2 \
& =\frac{3}{8} \mathrm{~m}\left(\frac{2 \pi}{\mathrm{T}}ight)^2 \cdot \mathrm{A}^2 \
& =\frac{3}{8} \mathrm{~m} \cdot \frac{4 \pi^2}{\mathrm{~T}^2} \cdot \mathrm{A}^2 \
& =\frac{3}{2} \cdot \frac{m \pi^2 A^2}{T^2} \
&
\end{aligned}$$

Answer

$$\frac{2 \mathrm{~m} \pi^2 A}{3 \mathrm{~T}^2}$$

Answer

$$\mathrm{\frac{3 m \pi^2 A}{2 T}}$$

Answer

$$\frac{2 \mathrm{~m} \pi \mathrm{A}^2}{3 \mathrm{~T}}$$

Answer

$$\frac{2 \mathrm{~m} \pi^2 \mathrm{~A}^2}{2 \mathrm{~T}^2}$$

Oscillations

A bob of simple pendulum of mass 'm' perform $\mathrm{SHM} with amplitude '\mathrm{A}' and period 'T'. Kinetic energy of pendulum of displacement x=\frac{A}{2}$ will be

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