Demo 09-04 Pump Pendulum

A pendulum model of a child swinging is formed from a mass hanging on a string that passes over a pulley and is attached to a fixed point. If the pendulum is started into motion with a small amplitude, it can be "pumped up" to a large amplitude in much the same way that a child pumps a swing. When the swing is at the low point of its oscillation, the support rope is gently pulled, decreasing the length of the pendulum and raising the center of mass of the weight representing the swinging child. This raising of the center of mass is what a child does when "pumping" the swing. When the radius of the pendulum gets shorter, conservation of angular momentum results in an increase in the speed of the swinging mass, adding mechanical energy to the swing and thus allowing it to rise higher.A more complete and exacting description of pumping a swing suggests parametric instability as the principal concept