[01] Ahammodullah Hasan, Department of Mathematics, Islamic University, Kushtia, Bangladesh. [02] M. Abul Kawser, Department of Mathematics, Islamic University, Kushtia, Bangladesh. [03] Md. Mahafujur Rahaman, Department of Computer Science & Engineering, Z. H. Sikder University of Science & Technology, Shariatpur, Bangladesh.

In this paper, an extension of the Krylov-Bogoliubov-Mitropolskii (KBM) method (which is also regarded as one of the most convenient and widely used methods for investigating the transient behavior of nonlinear systems) is used to figure out the solutions of fifth order more critically damped nonlinear systems. To this end, the analytical approximate solutions of fifth more critically damped nonlinear systems are considered in which the three eigenvalues are identical and another two are different. In this article, we suggest that the perturbation solutions obtained by the extended KBM method adequately matches up with the numerical solutions.

KBM Method, Analytical Solution, More Critically Damped, Nonlinearity, Eigenvalues

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