Chaos and Order in the Damped Forced Pendulum in a Plane

parameters of the trajectories

time (s)

25

number of trajectories

16

parameters of the pendulum

length ( m )

2

mass ( kg )

1

acceleration due to gravity

gravity  m/

2

s



9.81

resistance of the fluid

resistance ( kg/s )

1.11

external force applied to pendulum

amplitude ( N )

11.46

frequency ( rad/s )

1.48

Apparently simple physical systems often have very complex behavior, as in the case of the damped forced pendulum in a plane, which can have chaotic or nonchaotic behavior. To show this, this Demonstration displays in one graphic various trajectories for distinct initial conditions restricted to a small zone.

In many cases all trajectories have the same form or have a regular form; in other cases the behavior is chaotic, and it is not difficult to see period doubling in the graph.