A simple pendulum of length L has mass M and | vedclass

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(A) The potential energy of a simple harmonic oscillator is given by the formula $U = \frac{1}{2} k A^2$,where $k$ is the force constant and $A$ is th

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$\frac{M g A^2}{2 L}$

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(A) The potential energy of a simple harmonic oscillator is given by the formula $U = \frac{1}{2} k A^2$,where $k$ is the force constant and $A$ is the amplitude.For a simple pendulum,the restoring force is $F = -Mg \sin 	heta \approx -Mg 	heta$ for small angles.Since $	heta = \frac{x}{L}$,the force is $F = -\frac{Mg}{L} x$.Comparing this with $F = -kx$,we get the force constant $k = \frac{Mg}{L}$.Substituting $k$ into the potential energy formula: $U = \frac{1}{2} (\frac{Mg}{L}) A^2 = \frac{MgA^2}{2L}$.

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is $(g =$ acceleration due to gravity$)$

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