Students, in groups of no more than three, are to model and analyze a given physical system using the tools and techniques learned in this class. It is expected that students will analyze their system using both analytical techniques as well as numerical methods.

The goal of this project is to illustrate the modeling, analysis, and simulation techniques learned in this class on a physical system. Each project must combine a mechanical system with a component of a different physical nature, for example, electrical or hydraulic. An example would be a mechanical system driven by a servo motor, containing its own internal dynamics relating the input voltage to the driving torque. In additin, you must present both analytical and numerical results.

Each report will be organized as follows:

• Introduction-what are you doing and what information will you obtain;
• Modeling-identify appropriate modeling assumptions and develop the equations of motion which correspond to the assumptions made;
• Linear Analysis-linearize the above model about some operating point (if necessary) and analyze the resulting behavior predicted by the model;
• Simulation-use MATLAB to verify the analytical predictions of both the qualitative and quanitative behavior;
• Conclusions-model extensions, including the validity of the constitutive assumptions, discussion of results, effect of modeling assumptions, etc.

The idea is for you to figure out how your system is going to behave. For example, what happens as the parameters vary, what happens when the initial conditions are varied, how will the predicted dynamics vary with modeling assumptions, etc. You will employ both analytical techniques (modeling and solving the equations in closed-form) as well as numerical methods (MATLAB) to solve the equations of motion.