You have seen in lecture and exercises how to model a forced spring-mass system with damping. The mathematical model for the charge on the capacitor in an LRC circuit is exactly the same:
Compare your results with the graphs on pages 286 and 287 in your text.
Plot some solution curves for this model in the plane. For simplicity (and sanity), choose parameter values C=1 and L=1. How do the solutions change with R?
Do some numerical studies of the van der Pol circuit. For simplicity, take C=1 and L=1 as in the last part. Focus on how the solution changes for different values of the parameter .
The resulting limit cycles are sometimes called relaxation oscillations. Can you explain this terminology? (You may want to visit your favorite, and most relaxed, electrical engineer.)
© 1996 by Will Brother. All rights Reserved. File last modified on April 25, 1996.