MA 226: Ordinary Differential Equations


The nonlinear pendulum is given by the system of differential equations

x' = y, y' = -0.2y -sin x

where x measures the angle that the pendulum makes with the rest position of the pendulum (hanging straight down). This angle is measured in the counterclockwise direction.

In this animation you will see the motion of a solution curve of the nonlinear pendulum equation in both the phase plane and as x- and y(t) graphs. The goal is to determine the actual motion of the pendulum corresponding to this solution. Whenever the motion stops, indicate where the pendulum is at that moment by drawing a picture of the actual pendulum. As the motion resumes, indicate how the pendulum moves.

Click here to see the animation. Note: the "begin", "step", and "again" buttons do not work in this QuickTime animation. Use the "VCR controls" in the animation to stop and start the animation. You may have to close the navigation tools or location window to see these controls.