Go to CCP Homepage Go to Materials Page Go to Differential Equations Materials Go to Table of Contents
Go Back One Page Go Forward One Page

The Pendulum

Part 2: The Phase Plane

  1. In your worksheet you will find a definition of the gravitational constant g and starting values for mass m of the pendulum bob, damping coefficient b, and length L. The mass is set at 1 kilogram, the damping is 0, and the length is 1 meter. Plot the solutions of
  2. starting from rest with initial values of theta at 0.5 radians and at 2 radians. Do you see anything surprising in the plot? Explain what you see.

  3. Draw a direction field and phase portrait with the trajectories of the solutions in step 1. Do you see anything surprising in the plot? Explain what you see -- including the relationship between the solution curves and the trajectories.
  4. Add modest damping to the model, say, b = 0.2. Repeat steps 1 and 2.
  5. Experiment with various values of the damping coefficient. If necessary, change the time interval over which you are plotting. Describe your observations about damping.
Go to CCP Homepage Go to Materials Page Go to Differential Equations Materials Go to Table of Contents
Go Back One Page Go Forward One Page


Send comments to the authors <modules at math.duke.edu>

Last modified: March 24, 1998