# The Pendulum - Demonstrations

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The equation of the driven damped pendulum is

d^{2}x/dt^{2} + 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

- Demonstration 1 - Ideal Pendulum
- Demonstration 2 - Damped Pendulum
- Demonstration 3 - Driven Damped Pendulum - small amplitude oscillations
- Demonstration 4 - Driven Damped Pendulum - large amplitude oscillations
- Demonstration 5 - Driven Damped Pendulum - period doubling
- Demonstration 6 - Driven Damped Pendulum - chaos
- Demonstration 7 - Driven Damped Pendulum - Poincare section

[First Demonstration]
[Outline]

Last modified Wednesday, November 24, 1999

Michael Cross

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