You're getting very sleeping cause I'm pulling the string very slowly

A pendulum consists of a point-mass object of mass \(m\) suspended from a pivot by a massless string of length \(L\). The pendulum is swinging freely in the vertical plane. By what factor does the amplitude of oscillation change if the string is very slowly shortened by a factor of \(k=2\)?

Details and assumptions

The amplitude of oscillation is very small.

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