# An Oscillating Pendulum

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The equation for a swinging pendulum is , where is the angle of the pendulum at time , is the acceleration due to gravity, and is the length of the pendulum arm. The linearized approximation replaces by , which is valid for small .

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Contributed by: Stephen Wilkerson (March 2011)

(United States Military Academy West Point, Department of Mathematics)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This is the example An Oscillating Pendulum from [1], Section 1.4, Modeling with First Order Equations. The equation can be solved numerically using NDSolve in *Mathematica*.

Reference

[1] J. R. Brannan and W. E. Boyce, *Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications*, New York: John Wiley and Sons, 2010.

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