Modelling a pendulum using differential equations     03/10/16

 

A most interesting intellectual exercises for anyone with a mathematical mind is to model the swing of a pendulum using differential equations. We know that the two forces that act upon a pendulum are the damping force Fdamping=-cx’and the restoring force Frestoring=-kx. When we combine this with Newton’s second law, we get mx”=-cx’-kxwhich can be rearranged to make the following second order differential equation mx”+cx’+kx=0. We can then use any solution method to solve for this differential equation