Derivation of the Matrix Equation for a Translational Mechanical System with Three Degrees of Freedom

Abstract

Several researchers have carried out derivation of equation of motion of mechanical systems with more than one degrees of freedom of movement using different approaches among which is the work of Sivak and Darina[11] who derived the equation of motion of a translational mechanical system with two degrees of freedom using Newton’s second law. This paper, therefore, provides an extension of the work of Sivak and Darina[11] to model a three degree of freedom translational mechanical system. The free-body diagrams of the individual masses are developed and then Newton’s second law applied. Finally, the three equations derived are presented in matrix form in order to solve the systems vibration problems.