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To model the pumping of a swing using conservation of angular momentum.
Variable length pendulum with pulley on stand, as shown.
Start the pendulum mass oscillating with a small amplitude. When the pendulum gets to its lowest position,pull gently down on the rope, shortening the pendulum and thereby increasing its velocity. Release the rope as the pendulum nears its high point. According to a possibly oversimplified analysis, conservation of angular momentum at the low point, before and after the pull is applied, explains why this procedure causes the amplitude of the swing to increase with time. See also discussion of parametric resonance.