A 27kg child sits on a 1.8-m-long rope swing. You are going to give the child a small, brief push at regular intervals.
If you want to increase the amplitude of her motion as quickly as possible, how much time should you wait between pushes?
Old Science Guy
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you want to apply the pushes in sync with the natural frequency and period of the swing
T = 2 pi sqrt(l/g) = 2 pi sqrt(1.8/9.81) = 2.7 s to 2 sig figs
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Steve
You must push at the natural period of the pendulum:
T = 2π√[L/g] = 2.7 sec