Modelling oscillatory systems

Theory and experiment have underpinned the study of physics for a very long time. Lately, a new tool has been added to the physicist’s toolbox - that of computer simulation of physical systems. Fast computers and high-level languages such as Java have spurred an interest in modeling physical systems.Our study models oscillatory phenomena. We simulate free, forced and coupled oscillations including resonance. We provide a numerical solution to the exact differential equation of a driven, damped pendulum (that is, driven by an external force) which is non-linear and does not lend itself to a solution by analytic means. The simulations are executed through the numerical integration of the differential equation of oscillatory motion by the Runge-Kutta method. The simulation is run for various driving forces and Q-Factors and the boundary between periodic and chaotic motions are investigated.The numerical integrator is written in Java. We use the Java Open Source Physics library for the purpose of animating the model as well as to enter and display data.The study demonstrates the infinite ease in executing a what-if analysis once a simulation is successfully set up without spending immense quantities of time, energy and money as would certainly be the case in carrying out a comparable exercise in a conventional laboratory.The study also demonstrates that real life animations of physical systems cannot be realized unless one uses the laws and equations of physics, which after all govern the behavior of such systems.