This applet mimics the movement of a pendulum.  Using the Euler Method and ordineary

differential equations, I was able to show how a pendulum would move with certain variables set by

the user.  These variables are:

    - Position (in radians)

    - Frictional Force (a value between zero and two is recommended)

    - Driving Force (a value between zero and two is recommended)

    - Length of pendulum arm (a value between 3 and 11 is recommended so that it can still be viewed on screen)

    -Initial Angular Velocity (how fast the pendulum initial rotates about the origin)

    This diagram shows the direction of positive radians.  Theta represents

the position.  Entering Pi for theta (position) will put the pendulum almost perfectly upside down.

Directions:

    Press the Start button to begin the animation with the initial variables (see below).  To enter new values, without stopping the animation or clock, simply put the values into the corresponding fields and press the Enter New Values button.  This will keep the animation going, but with different conditional values.

    You can drag the pendulum with the mouse to a new initial position.  All the other variables will remain the same.

    The Reset button is used to stop the animation and reset the clock.  It will reset the animation to whatever values are entered in the fields.  You can enter new values, press Enter New Values, and then Start to see the new animation.

 Initial Values:

Position = Pi/4

Frictional Force = .1

Driving Force = 0

Length of Pendulum Arm = 10

Initial Angular Velocity = 0

WARNING!

There is a small bit of error in the animation if it is played for a long period of time.  The pendulum movements aren't perfectly accurate because the Euler method has a large degree of error over a long period of time.

Documentation