Activities

1. 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.
2. 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.
3. 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?
4. Finally, investigate the simulation using the settings suggested in the Baker and Gollub book.