Advanced Numerical Simulation of Pendulum Dynamics: A Comprehensive Analysis of Environmental Influences and Non-Linear Behavior - Taufik, Muhammad; Sutrio, Sutrio (Fakultas Keguruan dan Ilmu Pendidikan, Universitas Mataram, 2024)
This study explores the intricate dynamics of pendulum motion by numerically simulating the influence of environmental factors, including temperature, pressure, and humidity. Employing a high-precision Euler method with a time step of 0.0001 seconds, a 1-meter-long pendulum was modeled under varying conditions: temperatures ranging from 0°C to 40°C, pressures between 950 hPa and 1050 hPa, and humidity levels from 20% to 80%. The simulation incorporated key factors such as thermal expansion, air resistance, and non-linear oscillatory behavior for initial displacements up to 30°. Results reveal that a 40°C rise in temperature induces a 0.0007-second change in period and a 0.001 m/s² variation in calculated gravitational acceleration, predominantly due to rod expansion. Conversely, the effects of pressure and humidity were found to be negligible. Non-linear analysis at a 30° initial displacement indicated a 0.5% increase in period compared to 5°, underscoring the impact of the initial angle on pendulum dynamics. The model demonstrated remarkable accuracy for small-angle oscillations, aligning within 0.01% of theoretical predictions and 0.1% of experimental data. These findings offer valuable insights into pendulum behavior under diverse environmental conditions, providing a robust foundation for advancing the design and calibration of precision instruments and timekeeping mechanisms.