Interactive Educational Modules in
Scientific Computing

Energy Minimization

This module graphically demonstrates the natural minimization of energy by a mechanical system, specifically a mass-spring system.

A mass is suspended from one or two springs. The user can set the mass into motion by pulling it with the mouse. Upon release, the mass will then move in response to the combined forces of the springs and gravity. Eventually it comes to rest at a point of minimum potential energy. Note that the system will be in equilibrium when the force, which is given by the negative gradient of the potential, is zero, i.e., at a critical point (specifically a minimum) of the potential. A number of parameters are user selectable, including the size and shape of the mass, the spring constants and lengths, the acceleration due to gravity, the damping factor, and the number of springs (1 or 2), as well as various controls over the animation.

Reference: Michael T. Heath, Scientific Computing, An Introductory Survey, 2nd edition, McGraw-Hill, New York, 2002. See Examples 6.1 and 6.4.

Developers: Jeffrey Naisbitt and Michael Heath