The equation of motion for a damped, sinusoidally driven pendulum in the earth's gravitational field is,
m L d2q/dt2 + g dq/dt + m g sin q = A sin( w t)
where q is the angle with respect to the vertical, m is the mass, L is the length, g is the acceleration of gravity and g is the damping. The driving force has amplitude A and driving frequency omega, w. Choosing units such that m, L, and g are all one, i.e., so called scaled units, simplifies the equation to:
d2q/dt2 + g dq/dt+ sin q = A sin( w t).
The Pendulum Physlet solves this differential equation using a 4th order Runge-Kutta algorithm.
Note: Click inside the applet and press the spacebar to stop the animation.
Press the tab key to clear the phase and time graphs. This is useful to remove transients.