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  4. In SHM restoring force is F = -kx , where k is force constant, x is displacement and A is amplitude of motion, then total energy depends upon

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Q. In $ SHM $ restoring force is $ F = -kx $ , where $ k $ is force constant, $ x $ is displacement and $ A $ is amplitude of motion, then total energy depends upon

MHT CETMHT CET 2007Oscillations

Solution:

In SHM, the total energy
$ = $ potential energy+ kinetic energy
or $ E=U+K $
$ =\frac{1}{2}m \omega^2 x^2 +\frac{1}{2}m \omega^2(A^2 -x^2) $
$ =\frac{1}{2} m \omega^2 A^2 =\frac{1}{2}kA^2 $
where, k = force constant= m $ \omega^2 $
Thus, total energy depends on k and A