A simple mechanical model to demonstrate a dynamical phase transition

The main aim of this paper is to discuss a dynamical phase transition from the wave propagation regime to a dissipative regime with a simple model. The spinodal instability originating from the properties of potentials may generate a dynamical phase transition. The stability point divides the processes into two parts with regard to their dynamics; the dynamical phase transition means a transition from one dynamics to the other one through this point. There are some well-discussed examples from physics like the sound wave propagation in the van der Waals gases, the so-called tachyonic phase transition in the cases of the relativistic Klein-Gordon equation, and especially in the modern field theories in general. This is the reason why we feel the necessity to point out the essence of this kind of phenomena in the education via suggestive models, too. In the present paper we show a simple mechanical model for the spinodal instability and the tachyonic phase transition; the latter example must be useful to get an insight into these processes.