Analysis of Motion Resisted by Friction. II. Velocity-Dependent Friction

An exact method for analysis of the motion of a practical frictional oscillator with velocity-dependent friction is presented. Exact solutions are presented for the cases of free and harmonic forced vibration. It is shown that the oscillator studied exhibits a behavior that, under certain conditions, is significantly different from that of the constant Coulomb oscillator. Under free vibration, the oscillator studied exhibits longer duration of motion and less permanent displacement, whereas under forced vibration it exhibits a much smaller number of stops per cycle and different frequency content. Some of these conclusions appear to be in agreement with experimental results.