We investigate the anharmonicity of a large amplitude pendulum and develop a novel technique to detect the high Fourier components as a function of the amplitude for large amplitudes close to 180°. The technique involves doing a Fourier analysis on each half-cycle of the amplitude versus time. The presence of the third and fifth harmonics is detected and the variations of the corresponding Fourier coefficients with amplitude are studied. The experimental setup is inexpensive and simple to implement.
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There is an apparent discrepancy between the results of the perturbation method, Eqs. (2), (3), (5), and (7), presented here and in Ref. 8 and the results of Ref. 11. If the typos in Ref. 11 are taken into account, the two results are the same. We are grateful to one of the referees for pointing out this apparent disagreement.
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Further details of our experiment and a copy of the MATLAB program for the Fourier analysis of the experimental results and for solving numerically Eq. (8) can be obtained from ⟨www.fisicarecreativa.com⟩.
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© 2008 American Association of Physics Teachers.
2008
American Association of Physics Teachers
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