Pendulum Phase Plane Applet
An updated version of this demonstration, without Java, is available
here.

This applet draws numerical aproximations to the phase curves for
the system of differential equations

This system is equivalent to the second-order equation
the equation of a pendulum.
Clicking on a any point in the applet begins a phase
curve at that point. The `Continue` button will continue a curve
from its final point. You may choose to use either Euler's method (drawn
in red),
a Runge-Kutta method of order 2 (drawn in green), or a Runge-Kutta method
of order 4 (drawn in blue).