Volume 33, No. 4, pp. 669-677, October 2007
Abstract. A simple perturbation technique is developed to investigate the critically damped nonlinear systems. Recently, Shamsul  has presented an approximate technique (based on the Krylov-Bogoliubov-Mitropolskii method) to solve similar critically damped nonlinear systems with small non-linearities. Only for certain initial conditions Shamsul's solution can be used when nonlinearity is significant. On the contrary, the new solution gives desired results for various initial conditions whether the nonlinearity is small or significant. Most of the cases the new solutions give better results than the existing solutions obtained by Shamsul  and Sattar . The method has another merit that the initial condition equations for the variables can be solved analytically; but for the methods [2, 12] the same are solved by the numerical method. The method is illustrated by an example.
Received April 6, 2006.
AMS Subject Classification. 34E05.
Key words. non-oscillations, asymptotic solution, critical damping.