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The Pendulum

Part 4: Over the Top

We now think of the connection between the pivot of the pendulum and the bob as a very light ("massless") but inflexible rod rather than a string. We continue to assume there is no damping.

  1. Explain why the pendulum has an unstable equilibrium at theta = pi (or any odd multiple of pi) and theta' = 0.

  2. Experiment with starting values of theta and theta' that should make the pendulum bob go "over the top". Plot both solutions and trajectories, adjusting your scales as necessary to see the curves.
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Last modified: March 24, 1998