Laplace Equation

What does this Model Represent?

This model illustrates (and animates) the movement of an oscillating surface. For instance, this could represent a drumhead that has been struck. The center four squares in this model are the source of the oscillation, and as they vibrate up and down, the surrounding cells dampen the effect.

What are the elements of this Model?

Start - acts as a switch to determine when to run the model

• 1=on 0=off

Step - the time step to use in this model

Iteration - how long the model has been running

• This is automatically updated

Pulse - the value that will be used for the center square

• This is automatically updated

How do I use this Model?

• Enter 1 in the start field.
• Hold down the [ctrl] [=] buttons in order to run the model.
• Change the time step and run the model see how the vibration is affected.

What should I expect?

The center square on the graph should glide up and down, alternately creating a peak and a valley. The lower the time step, the more smoothly (and slowly) the animation will move.

Download the model file.