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The unified Krylov-Bogoliubov-Mitropolskii (KBM) method is used for determining the analytical approximate solution of a fourth order weakly nonlinear differential system with strong damping and slowly varying coefficients when a pair of eigen-values of the unperturbed equation is a multiple (approximately or perfectly) of the other pair or pairs. In a damped case, one of the natural frequencies of the linearized equation may be a multiple of the other. The analytical first order approximate solution for different initial conditions shows a good coincidence with those obtained by the numerical procedure. The method is illustrated by an example. Key words: Perturbation method; Weak nonlinearity; Oscillatory process; Strong damping; Varying coefficients DOI: 10.3329/jbas.v34i1.5493 Journal of Bangladesh Academy of Sciences , Vol.34, No.1, 71-82, 2010

Approximate Solution of a Fourth Order Weakly Non-Linear Differential System with Strong Damping and Slowly Varying Coefficients by Unified KBM Method