  The Simple Pendulum
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.
$\displaystyle{ E = \frac{1}{2} m L^2 \omega^2 + m g L (1 - \cos \theta) }$; $m = 1 \text{ kg}$ Initial angle $\theta_0$ of the mass: rad0 ≤ $\theta_0$ ≤ 0.4 rad Value of $g/L$: Initial angular velocity $\omega_0$ of the mass: rad/sec0 ≤ $\omega_0$ ≤ $\pi$ rad/sec Time-step $\mathrm{d} t$ of the system: sec0.001 ≤ $\mathrm{d} t$ ≤ 0.1 sec Period of the pendulum: sec
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