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Analytical Solutions of Fourth Order Critically Damped Nonlinear Oscillatory Systems with Pairwise Equal Complex Eigenvalues

M. Abul Kawser, Md. Mizanur Rahman, Md. Mahafujur Rahaman


In this paper, we have considered asymptotic solutions, when the four eigenvalues are pairwise equal and complex by modifying the Krylov-Bogoliubov-Mitropolskii (KBM) method, which is regarded as one of the most widely used method for studying the transient behavior of oscillating systems. We apply successfully the modified KBM method to obtain the solutions of fourth order critically damped oscillatory nonlinear systems. It is shown that the solutions obtained by the modified KBM method satisfactorily correspond to those obtained by the numerical method using Mathematica.


KBM method, critically damped oscillatory system, nonlinearity, eigenvalues.

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