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1 results

  • Project 3: - Pendulum as a Standard of the Unit of Time

  • Pawel Scharoch, Wrocław University of Science and Technology, Maciej P. Polak, University of Wisconsin, Madison, Radosław Szymon, Wrocław University of Science and Technology
  • Software developed by Katarzyna Holodnik-Malecka, Wrocław University of Science and Technology
  • Book:
    A First Guide to Computational Modelling in Physics
    Published online:
    01 February 2024
    Print publication:
    08 February 2024, pp 18-25

  • Summary

    This project focuses on the Initial Value Problem (IVP) for ordinary differential equations with the application of multipoint recursion schemes. The effectiveness and convergence of these schemes are explored and subsequently applied to examine the properties of a compound pendulum, specifically the dependence of the oscillation period on energy. The chapter then focuses on Newton’s laws of motion, laying the foundation for understanding the motion equation. The project uses a simple pendulum to illustrate the concept, looking at how changes in amplitude affect the period of harmonic oscillations. Numerical methods, such as recursive methods based on local extrapolation, are then employed to derive formulas. The project concludes by discussing the integration of Runge–Kutta methods and implicit schemes to solve the equations. This project ultimately questions the viability of the pendulum as a standard unit of time, adding value to ongoing discussions in physics and mathematics education.