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WOLFRAM|DEMONSTRATIONS PROJECT

The Pendulum: From Simple Harmonic Motion to Chaos

​
pendulum attributes
damping and driving force attributes
runtime settings
appearance options
pendulum length L
0.2
initial angular displacement θ
0
0
initial angular speed ω
0
0
run
force
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
angular displacement θ
angular speed ω
phase space
​
time
angular
displacement θ
θ(t) plot
​
L =
0.2
θ
0
=
0
ω
0
=
0
D =
0
A
F
=
0
ω
F
=
0
ϕ
F
=
0

A pendulum consisting of a mass fixed to the end of a (massless) rod can exhibit complicated motion when driven by an external force and with possible damping. This Demonstration explores the range of resonant, transient and chaotic behavior that this simple system can exhibit. After selecting the various parameters, click the "run" arrow to set the pendulum in motion.