A simple pendulum of length $L$ has mass $m$ and it oscillates freely with amplitude A. At extreme position,…

A simple pendulum of length $L$ has mass $m$ and it oscillates freely with amplitude A. At extreme position, its potential energy is ( $\mathrm{g}=$ acceleration due to gravity)
  1. $\frac{m g A}{2 L}$
  2. $\frac{\mathrm{mgA}^2}{\mathrm{~L}}$
  3. $\frac{\mathrm{mgA}}{\mathrm{L}}$
  4. $\frac{\mathrm{mgA}^2}{2 \mathrm{~L}}$

Solution

Potential energy of particle at extreme position is, $\begin{aligned} \text {,P.E. } & =\frac{1}{2} m \omega^2 A^2 \\ & =\frac{1}{2} m \times \frac{g}{L} \times A^2 \quad \ldots\left(\because \omega=\sqrt{\frac{g}{l}}\right) \end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 1)

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