Abstract
We study the dynamics of a discretized model of an elastic bar in a hard device formed by a chain of point masses connected by nonlinear springs whose total length is a controlled parameter. We compare the description of the system dynamics given by the first-order (gradient) dynamics, the second-order (Newtonian) dumped dynamics and the Relaxation Oscillation Theory. Using a technique based on Liapunov's second method, we prove a dynamic stability result concerning the above-mentioned ODEs.