A New Accurate Formula for the Large-angle Period of a Simple Pendulum
Mohammed Bechiri *
Department of Mechanical Engineering, Faculty of Sciences and Applied Sciences, University of Larbi Ben M'Hidi, Oum El- Bouaghi, 04000, Algeria.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a numerical solution of the nonlinear differential equation governing the non-sinusoidal oscillatory motion for the large angle period of a simple pendulum. The numerical method is based on the discretization of motion equation according to an explicit finite difference scheme. Also, an approximation formula giving the period on the large oscillations amplitude is developed and compared with the numerical model. The results showed a good agreement with a deviation less than 0.063%. The simple pendulum consists of a point mass attached to a massless and inextensible wire that is fixed at the upper end. The oscillations period value is calculated with a precision order of the one-tenth of the millisecond. The approximation formula developed in this work is simple, flexible and more accurate than other formula available in literature.
Keywords: Simple pendulum, nonlinear equation, numerical resolution, approximation formula