Existence of periodic solutions for a mechanical system with piecewise constant forces

Abstract

In this study, we consider spring-mass systems subjected to piecewise constant forces. We investigate sufficient conditions for the existence of periodic solutions of homogeneous and nonhomogeneous damped spring-mass systems with the help of the Floquet theory. In addition to determining conditions for the existence of periodic solutions, stability analysis is performed for the solutions of the homogeneous system. The
Floquet multipliers are taken into account for the stability analysis [3]. The results are stated in terms of the parameters of the systems. These results are illustrated and supported by simulations for different values of the parameters.

Keywords

• Generalized piecewise constant forces,spring-mass system,stability and periodic solutions

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