(untitled) (Journal of Bangladesh Academy of Sciences, 2011)
To obtain the second order approximate solution of a third order weakly nonlinear ordinary differential system with strong damping and slowly varying coefficients modeling a damped oscillatory process is considered based on the extension of a unified Krylov-Bogoliubov- Mitropolskii (KBM) method. The asymptotic solution for different initial conditions shows a good coincidence with those obtained by the numerical procedure for obtaining the transients response. The method is illustrated by an example. DOI: http://dx.doi.org/10.3329/jbas.v35i1.7973 Journal of Bangladesh Academy of Sciences, Vol.35, No.1, 77-89, 2011