ON PERIODIC MOTION OF SIMPLE PENDULUM: "AND YET, IT MOVES
Keywords:
FFT Analysis, Period Oscillation, Energy Conservation PrincipleAbstract
For solving the nonlinear differential equation of the pendulum, here we adopt a method that transforms the nonlinear differential equation into an equivalent linear one and then evaluate the period oscillation. We also apply the energy conservation principle to find the dependence of the time period on the amplitude of oscillation. Also harmonic balance method is applied to find an expression for the period of oscillation. Theoretical curves, simulation results and experimental results are given in support of the findings. Nonlinear method 1 proves that the pendulum oscillation is periodic but it has also very small amount of third harmonic. FFT analysis has been carried out of the data as obtained from the simulation results and it is found that system is almost free from harmonic distortion.
References
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Lima F.M.S. (2008). “Simple ‘log formulae’ for pendulum motion valid for any amplitude,” Eur. J. Phys., 29, pp 1091–1098. 2005.
Mohammed Y. Kamil, Ali Abid D. Al-Zuky, Radhi Sh. Al-Tawil "Study of Experimental Simple Pendulum Approximation Based on Image Processing Algorithms" Applied Physics Research Vol. 3, No. 1; May 2011
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Copyright (c) 2019 B.N. Biswas, S. Chatterjee , S. Pal , S Guha Mallick (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
