I am ashamed to tell you to how many figures I carried these computations, having no other business at the time.Isaac Newton, after computing the natural logarithm of $1 + x$ to more than 50 decimal places

How can we determine the period of a pendulum that is not already in motion? The obvious way is to disturb the system and observe the resulting behavior. It can be found that the response of a system to perturbation can tell us something about the nature of that same system in the absence of a disturbance. As such, this illustration is an extension of The Simple Pendulum.

Motion of a Driven Damped Linear Oscillator

This program solves the equation of motion of a driven damped linear oscillator to illustrate how a harmonic system responds to perturbation.

$\displaystyle{ \sum F_x = m a_x \rightarrow A_0 \cos (\omega t) - k x - \gamma \frac{\mathrm{d} x}{\mathrm{d} t} = m \frac{\mathrm{d}^2 x}{\mathrm{d} t^2} }$