A New Accurate Formula for the Large-angle Period of a Simple Pendulum
Asian Journal of Physical and Chemical Sciences · pp. 1–10 · Published 5 Jan 2022
10.9734/ajopacs/2022/v10i130146Abstract
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.
References (12)
- 1 Physics for Scientists and Engineers with Modern Physics [DOI]
- 2 Classical dynamics of particles and systems [DOI]
- 3 A simple formula for the large-angle pendulum period [DOI]
- 4 An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime
- 5 Theoretical and experimental study of the motion of the simple pendulum [DOI]
- 6 Approximations for the period of the simple pendulum based on the arithmetic-geometric mean [DOI]
- 7 Simple ‘log formulae’ for pendulum motion valid for any amplitude [DOI]
- 8 Simple pendulum approximation [DOI]
- 9 Approximation for a large-angle simple pendulum period [DOI]
- 10 The Large-Angle Pendulum Period [DOI]
- 11 An Approximate Expression for the Large Angle Period of a Simple Pendulum
- 12 Simple Linearizations of the Simple Pendulum for Any Amplitude
Cited by 0
No indexed citations yet.
Related research
- Thermal and Fluid Effects of Non-Newtonian Water-based Nanofluids on the Free Convection Flow between Two Vertical Planes — shares topic coverage
- Analyzing a New Third Order Iterative Method for Solving Nonlinear Problems — shares topic coverage
- Formulation of a Connection for Prolongations and an Application to the Burgers-KdV Equation — shares topic coverage
Article metrics
Real usage data collected on this platform.
44
Page views
0
PDF downloads
12
Outbound clicks
0
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.