Revisiting Pendulum Motion Analysis with Varying Gravitational Acceleration
Giorgio Gambirasio, Denise Consonni · 2023
Although longtime known, mathematical modelling of a pendulum using Newton’s gravitational equation may have not received its due attention. There are causes for that. Considering that such modelling always results in non-linear differential equations, not analytically solvable, this is certainly one of the causes, driving scientists to search for possible simplifications.When technological advances gave researchers computer programs capable of numerically solving these non-linear equations, effectively removing the first cause, the same advances also produced improvements in the measurement of time and of gravitational acceleration (one of the utilities for pendulums) so that these devices have lost their usefulness as experimental instruments and consequently as subjects of interest to scientists as possible research field. There is a third cause: pendulums on Earth are always too short for the mentioned non-linearity to manifest itself, because the assumption of a constant gravitational acceleration g is sufficient to arrive to more manageable models.This paper is a revisitation of pendulum motion analysis using Newton’s equations, not restricted to constant gravitational acceleration g. A numerical example is solved, and plotting of angles, forces and energies is presented. Furthermore, the analysis is replicated when a non-conservative effect on pendulum motion is considered, namely the air friction.