The oscillatory motion of a mass suspended on a spiral spring is a standard application of second order linear differential equations in undergraduate mathematics subjects, and a commonly used illustration of simple harmonic motion and damped oscillations in physics texts. This topic is often a significant milestone for mathematics students in particular, in that it opens the door to the world of modelling with differential equations. Analysis of measurements of standard undergraduate laboratory springs reveals that none of these assumptions are met, and that it is quite difficult to model accurate measurements of damping coefficients and period of oscillation.
Some key findings are as follows.
Hooke's law is a good approximation to the elastic behaviour for extensions of up to 3 l 0 but nonlinear behaviour is detectable using standard undergraduate laboratory technique of measurement by eye using a 1mm graduated ruler. With care, a bob can be released from rest so that it oscillates with motion sufficiently close to rectilinear that spurious motion can be ignored. The period is virtually independent of amplitude of oscillation for amplitude up to one fifth of the length of the static spring. The period is temperature dependent. Exponential damping decay is observed in some circumstances such as for a sphere of radius up to about 7cm with amplitude of oscillation less than 2cm.