The bouncing ball
an MBL demonstration of the period doubling approach to chaos

Lei Bao
Physics Education Research Group
University of Maryland 

* sponsored in part by NSF grants RED-9355849 and DUE-9455561


Context of the experiment

The advantages of the bouncing ball experiment

We try to construct a simple experiment that can easily work in a hands-on lab class.

The experiment of a ball bouncing on an oscillating platform is a very appropriate one.

Previous research done by others

The bouncing ball experiment is famous and well studied. Many researchers have done excellent jobs on this topic.

The bouncing ball laboratory

In order to implement the bouncing ball experiment as a lab, we incorporated some new methods into the traditional experiment.

Experiment setup

Interfacing with ULI

The major activities in the experiment

The two activities that we are looking for in the lab are to

Typical trajectories of simple orbits

Typical 1-T orbit

Typical 2-T orbit

Relation between the period and the amplitude of the pulse

The relation between the period for stable even mode orbits and the amplitude of the pulse generated by the collision is:

Consider the 1-T and 2-T orbits. The ball in a 2-T orbit stays in the air twice longer than in a 1-T orbit, therefore the pulse generated in 2-T orbit should be twice as large.

The signal output shown on the computer

Period doubling

Shift mode of the 2-T period

Bifurcation diagram

Iterative process of research, instruction, and curriculum development