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In this paper, a new novel energy balance method based on the harmonic balance method is proposed to obtain higher-order approximations of strongly nonlinear problems arising in engineering. Especially, second-order approximation is considered in this paper. Results found in this paper are compared with the exact result and other existing results. The results show that the proposed method gives better result for both small and large amplitudes of oscillation than other existing results. The method is illustrated by examples. It has been shown that the proposed method is very effective, convenient and quite accurate to nonlinear engineering problems.