Recently Shen suggested a modification of He’s frequency formulation using Lagrange interpolation with great success for the cubic-quintic Duffing oscillator. This paper proposed an alternative modification of He’s frequency formulation by dividing the oscillators into two extreme conditions when the amplitude is either extremely small or remarkably large, and He’s frequency formulation is used for each case, and a final frequency formulation is obtained by matching the two extreme conditions. Comparison of the approximate frequency with the exact one for various amplitudes shows good agreement.
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Hongjin Ma (2022) studied this question.
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