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Chaotic Oscillations: Magnetic Pendulum

A pendulum with magnetic tip swings above an array of four magnets on a transparent base (suitable for an overhead projector). The system has four stable equilibrium points, and the force is highly nonlinear. When started with large amplitude, the pendulum quickly decays from a nearly periodic orbit into a chaotic orbit about the four magnets, and eventually gets “stuck” in small oscillations about one of the magnets. Since a chaotic system is highly sensitive to initial conditions, it is difficult to predict which of the four magnets will eventually trap the pendulum, no matter how careful you are to release the pendulum from the same place each time.

Chaotic Oscillations: Magnetic Pendulum