Some systems show a marked change in behavior as parameters change. For example, a damped harmonic oscillator with exhibit over damped, under damped, or critically damped behavior depending on the values of mass, spring constant, and damping constant specified.
Other system behave distinctly different with different initial conditions, for example, a pendulum will nearly match its linearized analytical solution when started from rest with a very small angle, and it will match less and less well as the initial displacement is increased.
What different behaviors can the system you have chosen exhibit with different initial conditions and different parameter combinations. You should plan to exercise several different combinations. For example, a two-mass system, either connected by springs or as a double pendulum, may move with the motions of both masses in phase or out of phase Make a table with initial conditions and parameters as row labels, different behaviors as column labels, and populate it with the appropriate values. For examples: Select a system that can be described by an ordinary differential equation of third order or higher, or by a system of ODEs of equivalent order. The damped harmonic oscillator and single pendulum are not options, because they are only second order and we have already modeled them in lab. Your textbook may have some interesting candidates. Other suggestions include: double pendulum, bicycle, multiple-spring-mass system, etc. See also:
• https://www.ohio.edu/people/williar4/html/PDF/ModelTFAtlas.pdf
• https://www.jirka.org/diffyqs/htmlver/diffyqsse21.html
Requirements:
1. You must be able to model the system with the MATLAB tools we have developed in class.
2. You must be able to be confirmed, verify, or validate the results of your analysis in some way.