Very Large Angular Oscillations (Up to 3π/4) of the Physical Pendulum—A Simple Trigonometric Analytical Solution

Joao C. Fernandes ()
Additional contact information
Joao C. Fernandes: Physics Department, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Mathematics, 2025, vol. 13, issue 17, 1-21

Abstract: The oscillatory properties of pendular motion, along with the associated energetic conditions, are used to induce analytical functions capable of simultaneously describing the angular position and velocity. To describe the angular position of a generic pendulum, for very large amplitudes of oscillation, we used the numerical solutions obtained from the numerical resolution of the differential equation of motion. The solver software needed was built using the LabView 2019 platform, but any other ODE solver containing peak and valley detectors can be used. The fitting software and plots were performed with the ORIGIN 7.0 program, but also other equivalent programs can be used. For a non-damped pendulum, an analytical model is proposed, built from simple trigonometric functions, but containing the important physical information of the dependence between the period and amplitude of oscillation. The application of the proposed model, using the numerical solutions of the non-approximated differential equation of motion, shows very good agreement, less than 0.01%, for large amplitudes, up to 3π/4.

Keywords: undamped pendulum; very large angular oscillations; friction; damped oscillator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/17/2836/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/17/2836/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:17:p:2836-:d:1740970

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().