Ehrenfest's famous Principle of Adiabatic Invariance states that the ratio of the energy of an oscillatory motion to the frequency stays constant. This principle can be demonstrated with a simple pendulum. Consider a simple pendulum executing small-amplitude oscillations. The string with negligible mass is shortened an amount Al very slowly, so that the change in amplitude from one oscillation to the next is negligible. Show that under these conditions, the ratio of the energy to the frequency remains constant.
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Ehrenfest's famous Principle of Adiabatic Invariance states that the ratio of the energy of an oscil...
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