Harmonic Oscillations with Sliding and Static Friction, Graphical Output of Curves

Abstract

In lectures on mechanics simple and coupled harmonic oscillations of point masses are covered in detail. One encounters various types of oscillation, depending on whether there is a driving force or not, and whether frictional forces are taken into account or not. The frictional forces are usually assumed to be forces dependent on the velocity. These first of all play an important role in physics, such as for example in the damping of galvanometers, and secondly they are capable of being handled analytically. Less amenable to analytic calculation are sliding and static friction, since they behave discontinuously at the turning point of an oscillation. Only piecemeal analytic solutions can therefore be obtained. To a computer it presents no difficulty to integrate across the discontinuities. We therefore take as our first physical example the motion of a point mass under the influence of a harmonic restoring force and under the influence of sliding and static frictional forces.