Chaos in a Pendulum

A damped physical pendulum with periodic forcing is a seemingly simple deterministic system (i.e., the equations of motion are known exactly) with surprisingly complex behavior. Tiny variations in the damping, forcing amplitude, or forcing frequency can send the pendulum from periodic into chaotic regimes, then back into a “window” of order, and again into chaos. This hallmark of chaotic systems – extreme sensitivity to initial conditions – eventually leads to loss of long-term predictability.