The Pendulum - Demonstrations

You can find more information on how to use the applets on the following pages (return here by hitting "Back"):

The equation of the driven damped pendulum is

d2x/dt2 + b dx/dt + sin x = a cos(ct) + d

In autonomous form with X=x, Y=dx/dt, Z=ct:

dX/dt = Y
dY/dt = -bY - sinX + a cosZ + d
dZ/dt = c

The parameters of the applet are a=g the strength of the oscillatory driving, b the dissipation strength, c the frequency of the external driving, and d an additional steady drive.

Demonstrations

  1. Demonstration 1 - Ideal Pendulum
  2. Demonstration 2 - Damped Pendulum
  3. Demonstration 3 - Driven Damped Pendulum - small amplitude oscillations
  4. Demonstration 4 - Driven Damped Pendulum - large amplitude oscillations
  5. Demonstration 5 - Driven Damped Pendulum - period doubling
  6. Demonstration 6 - Driven Damped Pendulum - chaos
  7. Demonstration 7 - Driven Damped Pendulum - Poincare section
[First Demonstration] [Outline]
Last modified Wednesday, November 24, 1999
Michael Cross

This page has been visited times.