Enhancing Student Understanding Of Mechanics Using Simulation Software

The wide availability of commercial codes, such as MAPLE®, has made it possible to significantly enhance the teaching of undergraduate courses in mechanics. New problems, usually non-linear, can be introduced which previously could not be treated because of the lack of analytic solutions. By means of numerical solutions to these problems, students can get a feel for finite difference approaches and, perhaps more importantly, their physical understanding can be enhanced and new phenomena explored. The following examples are presented with the underlying equations cast, as much as possible, into non-dimensional form: (i) a finite difference scheme, (ii) a non-linear pendulum subjected to various initial conditions, showing how the period depends on the amplitude, (iii) a non-linear softening spring showing the existence of instabilities, (iv) the stability of an inverted pendulum restrained by a spiral spring, illustrating the existence of multiple equilibrium states and their stability and (v) a numerical simulation of a sweep test (forced motion of a single-degree-of-freedom system in which the forcing frequency varies with time), showing that if the sweep rate is too fast, no resonances will be observed.