Application of a Heuristic Method to Solve Nonlinear Oscillators with Irrational Forces
Keywords:Nonlinear oscillators, Periodic solution, Approximate frequency, Conservative oscillator, Duffing-relativistic oscillator, Jacobi polynomials
AbstractThis paper applies another amplitude-frequency relationship as of late established by Yazdi and Tehrani (Alexandria Engineering Journal 54 99-103, 2015) to analyze periodical solutions of nonlinear oscillators; such oscillators are considered emphatically nonlinear on the grounds that they contain an irrational force term. Estimation strategy is straightforward yet additionally helpful and its formulation depends on combining the energy balance technique with an uncommon collocation point. At long last, we uncover the convenience and proficiency of the proposed technique resolving three instances of conservativeÂ nonlinear oscillators in which the maximum relative error acquired is $2.5\%.$ Exposed models show that the strategy has a high precision to solve mechanical issues of both small and huge estimations of the oscillation amplitude. Finally, the methodology used can be very useful for the study of nonlinear oscillators in basic undergraduate physics and mechanics courses.
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