Abstract
The ancient Chinese algorithm, also known as the method of surplus and deficiency that has been used by He to find the angular frequency of nonlinear oscillators, is adapted to derive the approximate frequency-amplitude equations of undamped forced cubic, cubic-quintic, and cubic-quintic–heptic oscillators of the Duffing-Type. The accuracy of the obtained frequency-amplitude equations is examined by comparing theoretical predictions with each Duffing-type oscillator’s numerical integration solutions. These examples show that the ancient Chinese algorithm is a powerful and easy-to-follow method to find the frequency of forced nonlinear oscillators.
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