Mathematics can be used to describe many physical phenomena. This resource has been designed to help show how the motion of a mass attached to the end of a spring, running along a frictionless table, can be described, predicted, and understood using a variety of mathematical techniques.

To gain a complete understanding of the mathematics, a simulator for a mass-spring oscillating system has been developed.

The mathematics behind the spring simulator is governed by a branch of calculus called Differential Equations. Although the tools required to work with differential equations are given in a High School calculus course, the combination of steps required is complex and is not often taught until post-secondary education. Consequently, there are many ways to approach this topic, so to accompany the spring simulator, four separate modules: Physics 20, Math 30, Math 31, and Math 201, have been created. Each module is has been developed to cater to the mathematical techniques taught in each of the courses which each module takes its name from.

Before working through any of the modules, it is recommended that you familiarize yourself with the simulator by exploring the simulator. Being able to use the simulator well will assist your understanding of the modules, and will aid you in working through the exercises that appear along the way. Each module is self-contained, so after you have explored the capabilities of the simulator, proceed to whichever module is appropriate for you. And of course, feel free to try a higher-level module if you wish!

If you would like to open a larger version of the simulator, click on the Simulator link in the menu above. If you need more help with the simulator, click here.

Content on this page requires a newer version of Adobe Flash Player.

Get Adobe Flash player


1. Any text in blue contains a link.
2. You can navigate through each module internally by using these arrows, which will appear at the bottom of each module's pages.

Alternatively, you can select any page you wish to visit by using the links at the top of any page.
3. This web site uses visual simulations designed in Adobe Flash, so you will require Adobe Flash Player Version 8 or higher. You can download the most current free version here.
4. To activate the Flash components, youss may need to click anywhere on the component, depending on what browser you use, and what version of Flash you have.

This module was written by Drew Hanson, Cole Zmurchok and Gerda de Vries for CRYSTAL-Alberta.