##
MA 226:
Ordinary Differential Equations

**
Question:**
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.