Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.Isaac Newton

A common example of a mechanical system that exhibits oscillatory motion is the simple pendulum. A simple pendulum is an idealized system consisting of a bob of mass $m$ attached to the lower end of a rigid rod of length $L$ and negligible mass. The default parameters of this program generate a stable numerical solution when simulating large amplitude oscillations.

Oscillations of a Pendulum

This program solves the equation for the total energy of a simple pendulum to illustrate conservation of mechanical energy for large oscillations.

$\displaystyle{ E = \frac{1}{2} m L^2 \omega^2 + m g L (1 - \cos \theta) }$; $m = 1 \text{ kg}$