In spring-mass systems, we have modeled the damping force due to internal friction in springs and due to air resistance as proportional to velocity and acting opposite to it. We have also used that model for the force of friction between the mass in a horizontal spring-mass system and the smooth surface upon which it is sliding.
For two surfaces in contact, modeling friction force as proportional to velocity is reasonable if the surfaces are lubricated, say, by a thin film of water. But if the surfaces are dry, then a better model takes the force of friction as constant in magnitude and acting opposite to velocity.
Model a horizontal spring-mass system using this model for dry friction. Does dry friction have the same effects on frequency of oscillation and on decay as the conventional model of friction? What differences, if any, do you observe? Do the notions of overdamping and underdamping still apply? Is the behavior you observe physically reasonable?
If you use any numerical solution tools (e.g., Euler, Heun, on Runge-Kutta), convince the reader that your numerical results are accurate!
If you decide to use Matlab, you may find the sign function useful. Type help sign for more information.
The final report is due in lecture at 2:30 p.m. on Wednesday, December 11. Project reports will be evaluated in your PLA section on Thursday, December 12.
© 1996 by Will Brother. All rights Reserved. File last modified on December 6, 1996.