First, turn off damping by setting q to a very large number (1000, for
instance) and turning off the driving torque by setting the amplitude
to 0. This gives us a simple pendulum. Set the initial angular
displacement (theta) to both large (e.g., 3 radians) and small (e.g.,
0.2 radians) to see the difference between large amplitude and small
amplitude displacements. Before running the simulation for the first
time predict what the phase space graph (the plot of angular velocity
vs. angular displacement) will look like.
Now, turn damping on by setting q to a smaller value (values between 2
and 20 work well). Leave the amplitude of the driving torque off so
the situation is a simple pendulum with damping. Again, predict what
the phase space graph looks like before running the simulation.
Now turn damping off (e.g., q = 1000) and turn on the driving torque.
What happens when you run the simulation now? Does changing the
driving frequency affect what happens?
Finally, investigate the simulation using the settings suggested in
the Baker and Gollub book.