Natural oscillations in approximately linear second order dynamic models

Abstract

Oscillations of second order non-linear dynamic models governed by <Mathematical Formula> are considered, where |∈ |is a small parameter. The perturbation methods based on small damping are applied to obtain approximate solutions of certain non-linear systems characterized by particular forms of <Mathematical Formula> As an application in Industrial Mathematics a special study is done on price fluctuations of a dynamic market model where the excess supply Qs - Qd is a quadratic function of the price trend. It is proved that an isomorphism between the dynamic market model and a classical dynamical damper exists and the price function converges to its intertemporal equilibrium price.