I was able to get the membrane vibration to work for a rectangular membrane. The equations are quite different for a circular membrane, so I'll need to write a new function for that. I'm still working on implementing this function into the GUI.
We recently covered vibrations of strings in my mechanical vibrations class. I decided to try and make a GUI to animate the vibration of the string. There are lots of options for changing the string properties and simulation parameters, as well as subjecting the string to various end conditions and combinations of initial conditions.
I hope to expand this simulation to animate 2-D membranes as well. It would be very cool to simulate how a drum head or the body of a violin vibrates in MATLAB.