The Damped Nonlinear Pendulum

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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.


Contributed by: Enrique Zeleny (September 2018)
Open content licensed under CC BY-NC-SA



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