Rubber Band - Cinderella Documentation
Description: The user's guide to the Interactive Geometry Software Cinderella

# Rubber Band

force** = **springconstant** ∗ **length

In CindyLab a rubber band is a Spring that has a resting length of zero. Rubber bands are constructed by a press/drag/release sequence as in the Add a Line mode. If the endpoints of the spring segment are not already present in the drawing, free masses will be added. A rubber band affects the two masses at the endpoints according to the formula

Here springconstant is a characteristic constant of the rubber band that can be adjusted in the inspector, and length is the distance between the two points. Thus if two mass-objects are at a certain distance from each other and connected by a rubber band, they will be attracted to each other. Since the attractive force is proportional to the distance of separation, the farther apart the masses are, the stronger the force.

If no global friction is present in the Environment, a system of masses and rubber bands will oscillate wildly. The following picture shows the situation of one free mass-point that is connected to a rubber band whose other end is tied to a regular (fixed) geometric point. The curve on the left shows the resulting oscillation of the point. (The curve was generated by the `drawcurves(...)` operator of CindyScript.)

Trace of a mass-point with unit velocity

If one uses the Environment to add some global friction, a damping of the oscillation will occur. In such a case, the system will converge to an equilibrium situation in which it comes to rest. The following picture shows a chain of masses connected by rubber bands under the influence of Gravity.

A chain of mass-objects and rubber bands under the influence of gravity

Networks of rubber bands exhibit interesting behavior. In a sense, such networks behave like spider webs. The following pictures show a gridlike arrangement of masses and rubber bands with various points pinned to the ground plane in the equilibrium situation.