You have seen in lecture and exercises how to model a spring-mass system with damping and external forcing. One application for the model is an automobile suspension system, where the forcing term is the road (with or without frost heaves) and shock absorbers provide the damping.
In this project, you will study the behavior of the solution with different types of damping terms. Recognize that once you allow the damping coefficient to depend on the solution, the equation is no longer linear and most analytic solution methods (such as characteristic equations and undetermined coefficients) are useless. You have no choice but to study the system through numerical methods.
How does the amplitude of the limiting solution depend on ? How does it depend on the initial data?
Compare your results with the graphs on page 280 and the formula given in Exercise 12 on page 282 in the text.
Do some numerical experiments with the Renault shock absorber. Explain in detail how you program the damping coefficient in your equation. Take for the forcing function and describe the limiting behavior of the solution for a range of values. Does the new shock absorber give a "smoother" ride than the original shock absorber? Do you think that Renault should pursue its development of this new shock absorber?
© 1996 by Will Brother. All rights Reserved. File last modified on April 25, 1996.