Periodic Solutions of Some Differential Equations that Show the Non-Linear Vibrations of the Mechanical Systems

Abstract

Many phenomenons of mechanical nature possess non-linear vibrations, their mathematical forming operation leading to differential equations or to systems of differential non-linear equations. In this work it is shown that we can determine aproximate analitical solutions for non-linear differential equations, such as &x& +e f ( x, x& ) + x = F ( t ) . We use the perturbations method for homogeneous and non-homogeneous for low parameters and we show that in special situations this equations are Van der Pol or Duffing equations.