See file here The file links to a paper entitled “Extracting the fingering and the plucking points on a guitar string from a recording”. Either explore the process (E12 project), or implement it (E71) in real time (E90)
Research Bond graphs – a technique developed for handling linear systems (mechanical, electrical…) under a single framework. https://en.wikipedia.org/wiki/Bond_graph
The dynamics of the voltage across a nerve membrane are well defined by a set of three coupled non-linear equations. MATLAB (or another tool) can be used to model these equations and accurately predict the dynamics of a nerve firing.
Make an animation (either MATLAB or web-based) of the inner ear example from class. This involved some simulation and some relatively simple graphics programming. You could also update and expand this web page (http://www.swarthmore.edu/NatSci/echeeve1/Ref/InEar/InnerEar.html) to include the animation.
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.
Use this method to make an animation (web-based?) that calculate pi. The Pi Machine – NYTimes.com.
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.
Recreating the THX Deep Note – Earslap. Read this blog post on how to create the THX Deep Note (the sound at the beginning of movies using THX). It involves some signal processing – see if you can do it in MATLAB. Here is professor Zucker’s implementation in shadertoy https://www.shadertoy.com/view
Right now, the signal generator is only configured to create sine waves and square waves. Code could be added to the U8903a GUI to enable the generation of triangle and Sawtooth waves.
Explore Fourier Transform and Filtering in 2 dimensions (i.e., images).
Put a heater on one end of a metal rod, and measure, predict and model the temperature along the length of the rod.
Read up on compartmental modeling and model some physiological system (e.g., glucose metabolism…)
Analyze and simulate the double pendulum without the small angle approximation. Include an animation.
Build an electronic analog computer (a circuit analog to Simulink) using integrators and summers….
Try to model the friction of the double pendulum experiment. The friction is closer to kinetic than viscous, so you’ll need a non-linear model (either your R-K, or simulink). This has some interesting aspects to it (as friction often does).
Put a heater in a box and try modeling the temperature in the box over time.
Build a small dial with a pointer and measure the transfer function of your hand as you try to follow a moving target.
Try to predict the deformation of a spider’s web with a spider sitting on it – you could model the web as springs and dashpots.
Record the audio impulse response (pop a balloon) and record the audio impulse response of various locations around campus. Play various sounds through the impulse response and explore the results.
We have a triple pendulum system – explore the modes of oscillation of this sixth order system, experimentally and in simulation.
Get data from double pendulum using a vision capture system.