Motion in Frictional Sliding Stick-Slip Oscillation

INTERMITTENT MOTION IN FRICTIONAL SLIDING STICK-SLIP OSCILLATION 

The behavior of the rider along the path BC can be analyzed exactly. The equation is that of damped harmonic motion with a constant resisting force added  

The following expression is introduced into Eqn 8-21 where Mg is the normal force due to a load of mass M and F. 

Inserting this into Eqn 8-21 and evaluating F from the load and the coefficient of kinetic friction, we get 

In the treatment above, stick-slip was discussed in terms of a real but very simple physical model. There are more sophisticated and detailed approaches which arise from the needs of engineering practice. For instance, B. R. Singh [14] represented the sliding system as shown in Fig. 8-6 and wrote the differential equation of motion during slip as 

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