The Damped Nonlinear Pendulum

The plots show the motion of a harmonic oscillator with damping, in phase space on the left and as a function of time on the right, with the position of the pendulum in the top-right corner. The equation of motion is , where is the natural frequency and is the damping constant. This equation does not take the form of the usual approximation .
Nonlinear analogs of underdamping and overdamping can be observed.
The second-order equation can be solved by splitting it into two first-order equations.

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