Spectral analysis and limit behaviours in a spring-mass system
M. Pellicer J. Solà-Morales
Communications on Pure & Applied Analysis 2008, 7(3): 563-577 doi: 10.3934/cpaa.2008.7.563
We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE.
keywords: Strongly damped wave equation decay of solutions overdamping. spectral analysis

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