Coupled spring equations for modelling the motion of two springs with
weights attached, hung in series from the ceiling are described. For the linear
model using Hooke’s Law, the motion of each weight is described by a fourthorder
linear differential equation. A nonlinear model is also described and
damping and external forcing are considered. The model has many features that
permit the meaningful introduction of many concepts including: accuracy of
numerical algorithms, dependence on parameters and initial conditions, phase
and synchronization, periodicity, beats, linear and nonlinear resonance, limit
cycles, harmonic and subharmonic solutions. These solutions produce a wide
variety of interesting motions and the model is suitable for study as a computer
laboratory project in a beginning course on differential equations or as an
individual or a small-groupundergraduate research project.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:tut/oai:encore.tut.ac.za:d1000896 |
| Date | January 2003 |
| Creators | Fay, TH, Graham, SD |
| Publisher | International Journal of Mathematical Education in Science and Technology |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | |
| Rights | International Journal of Mathematical Education in Science and Technology |
| Relation | Taylor & Francis |
Page generated in 0.0018 seconds