I compare two one-state-variable, rate-dependent, and state-dependent friction laws, that is, the slip law and slowness law, through the analyses of stability conditions based on a dynamic one-degree-of-freedom spring-slider model, subjected to such two kinds of friction. Results show that at low velocities, the stability criteria for the two laws are equal and similar to the steady-state criteria deduced by Ruina (1983). On the other hand, at higher velocities, the stability criterion for the slip law depends not only on the parameters of the friction law, but also on the sliding velocity and state variable of the system, whereas the stability criterion for the slowness law is the same as that at low velocities.

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