Explore modes on a drumhead – similar to modes on a guitar string, but in 2 dimensions.
Or – do a search for cloth physics.
This is very similar to the spider on a web project idea.
Check the video below. It is a simple pendulum, but reacts to magnets near the base. A non-linear problem to be modeled with RK – but not too difficult. http://en.wikipedia.org/wiki/Force_between_magnets#Magnetic_dipole-dipole_interaction
The animation system at http://lpsa.swarthmore.edu/Animations/ uses a fixed step size animation. Alter the code to use a variable step size.
Use the animation system (http://lpsa.swarthmore.edu/Animations/) developed by a student a few years ago to develop animations for some of the homework problems.
Use simulink and MATLAB together to simulate a system (and animate it). You could also do it all in MATLAB. The coupled pendulum system comes to mind.
Simulate the system shown using Runge-Kutta (it is nonlinear, but not too complex). http://en.wikipedia.org/wiki/Force_between_magnets#Magnetic_dipole-dipole_interaction
Z-Transforms are related to the Laplace Transform, but are used for discrete time systems (i.e., when a computer is used to sample a signal). This would be more research then physical.
It would be very nice to have a MATLAB gui that makes the audio analyzer output a series of impulses to a circuit and then have software that would add up the delayed and shifted impulse responses to create the output due to an arbitrary input. This is ambitious, but if you want a very software (MATLAB) intensive project – this might be it.