The parameters for the bouncing ball system should be determined before we continue our analysis. The relevant parameters, with typical experimental values, are listed in Table 1.1.
Table 1.1: Reference values for the Bouncing Ball System.
In an experimental system, the table's frequency or the table's amplitude of oscillation is easy to adjust with the function generator. The coefficient of restitution can also be varied by using balls composed of different materials. Steel balls, for instance, are relatively hard and have a high coefficient of restitution. Balls made from brass, glass, plastic, or wood are softer and tend to dissipate more energy at impact.
As we will show in the next section, the physical parameters listed
in Table 1.1 are related. By rescaling the variables, it is
possible to show that there are only two fundamental parameters in this model.
For our purposes
we will take these to be 
, the coefficient of restitution, and a
new parameter 
, which is essentially proportional to 
. The
parameter is, in essence, a normalized acceleration and it measures the
violence with which the table oscillates up and down.