One end of a chain is attached to the ceiling and the free end is given a sharp horizontal blow. The resulting pulse travels to the top of the chain, and a few seconds later the reflected pulse causes the free end to give a kick. The free end kicks again and again at regular intervals. The time between kicks is constant and has been accurately predicted by the solution of an ordinary differential equation. Close observation of the nature of successive kicks shows that they are not always in the same direction, but they do follow a pattern that repeats every four kicks. We have modeled this experiment by solving the wave equation with variable tension and summing the resulting series solution. The lateral deflection as a function of time and distance along the chain was calculated. The predicted deflection of the free end is in good agreement with experimental results obtained from a movie of the chain motion.

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Partial differential equations, Public policy and governance
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2000
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