Good historical sources for these behaviours are [2] and [5]. Of course, these behaviours strongly suggest nonlinearity, and in the late eighties, following recent and rapid progress in nonlinear analysis of boundary value problems that had just been taking place, I and co-workers attempted to give a mathematical explanation for these phenomena [13], [16-19]. Our starting point was that an unloaded cable cannot be described by the usual Hooke's law, since it resists expansion but not compression. Thus if an unloaded cable is expanded downward by a distance u from the unloaded state, the cable should have a resisting force ku+, in other words, ku if u is positive, and 0 if u is negative. When the cable is loaded, it stretches to a new equilibrium, around which it obeys the linear Hooke's law until deviations from equilibrium become large enough to result in loss of tension when the cable approaches the unloaded state. Using the tools of nonlinear analysis and numerical investigations, we showed that an equation for a nonlinearly supported beam with this type of nonlinearity could explain both large amplitude vertical periodic oscillations and the travelling wave behaviour. With the usual fervor of the newly converted, I suggested that the