the friction force abruptly changes sign at v = 0. The stiction F shows up as a larger spike at zero v than the dynamic friction value F d· Thus, this is a nonlinear friction function. It is multivalued at zero. In fact, at zero velocity, the friction force can be any value between -F and +F• It will be whatever force is needed to balance the system forces and create equilibrium. When the applied force exceeds F, motion begins and the friction force suddenly drops to F d· This nonlinear damping creates difficulties in our simple model since we want to describe our system with linear differential equations having known solutions.
Other sources of damping may be present besides coulomb friction. Viscous damping results from the shearing of a fluid (lubricant) in the gap between the moving parts and is considered to be a linear function of relative velocity as shown in Figure 10-Sb. Quadratic damping results from the movement of an object through a fluid medium as with an automobile pushing through the air or a boat through the water. This factor is a fairly negligible contributor to a cam-follower's overall damping unless the speeds are very high or the fluid medium very dense. Quadratic damping is a function of the square