Matrix Laplace Transform Method and It Applications on Spring-Mass Systems

Abstract

 There are several methods to solve an initial value problem of second-order homogenous linear systems of differential equations with constant coefficients. That are elimination method and matrix method. Whereas to solve nonhomogenous systems, used undetermined coefficient method and variation of parameter method, that through some difficulties and complex procceses. But then, there is an alternative method to solve it. It is Matrix Laplace Transform Method. The goals of the research are to explain Matrix Laplace Transform Method and use it to solve initial value problems of second-order homogenous linear systems of differential equations with constant coefficients. All of matrix entries are constant. The result of the research is be obtained solutions of second-order linear systems of differential equations with constant coefficients use Matrix Laplace Transform Method