Green’s Function and Periodic Solutions of a Spring-Mass System in which the Forces are Functionally Dependent on Piecewise Constant Argument

In this paper, damped spring-mass systems with generalized piecewise constantargument and with functional dependence on generalized piecewise constant argumentare considered. these spring-mass systems have piecewise constant forces of the formsax(ɣ(t)) and ax(ɣ(t))+h(t;xt ;xɣ(t)), respectively. these spring-mass systems are examinedwithout reducing them into discrete equations. while doing this examination, wemake use of the results which have been obtained for differential equations with functionaldependence on generalized piecewise constant argument in [1]. sufficient conditions forthe existence and uniqueness of solutions of the spring-mass system with functional dependenceon generalized piecewise constant argument are given. the periodic solution ofthe spring-mass system which has functional force is created with the help of the green’sfunction, and its uniqueness is proved. the obtained theoretical results are illustrated byan example. this illustration shows that the damped spring-mass systems with functionaldependence on generalized piecewise constant argument with proper parameters has aunique periodic solution which can be expressed by green’s function