Asymptotic boundary conditions in harmonic oscillators and applications

In this paper we present an analysis of the asymptotic behavior of damped and forced harmonic oscillators considering the (x2 , x . 2) representation , we find that from the analysis of the asymptotic behavior of boundary conditions , taking as an example the case of damped and forced harmonic oscillators, which its possible infer the dynamical behavior in this region for more complex systems, such as the nonlinear oscillator described in section 5.Some implications of the asymptotic solution for this system are discussed at the end of this section. However, a more detailed analysis of the analytical behavior of this system would be beyond the scope of this paper.