The approximate or exact analytical solutions for the differential equations which describe parametric free vibrations of mechanical systems

Abstract

The vibrations of many mechanical systems can be described by differential equations that have coefficients that depend on time. It is difficult to determine the approximate or exact analitical solutions of these equations. In this work, we show that we can obtain analytical exact or approximate solutions for non-linear homogeneous differential equations with variable coefficient which describes the parametric free vibrations of mechanical systems.