Vibration analysis of a mass on a spring by means of magnus expansion method

Abstract

In this paper, the differential equation for the motion of a mass on a spring is investigated, solutions of six different cases were analyzed and numerical solutions are obtained by means of Magnus Expansion Method. Any truncation of the Magnus series preserves qualitative geometric properties of the exact solution (Castellano et al. 2014). This is an important advantage of the Magnus expansion method. Therefore Magnus expansion method provides more accurate solutions than other frequently used numerical schemes. Finally the numerical results obtained by the present method and the analytical results were compared.