# 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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