Study of a unilateral oscillator with friction

We present a model for a nonlinear mechanical device which has a negative spring constant over a portion of its displacement range. It consists of a vertically compressed spring attached to a mass which is restricted to move on a horizontal rail. The motion is accompanied with friction, which is modeled by the Coulomb law. The model is formulated as a differential inclusion, and using standard results we show that it has a solution. Then we describe a numerical algorithm for the model and present numerical simulations of its behavior.