A suite of JAVA applets illustrating the mathematical analysis of the damped bouncing of an elastic ball. This is one item from a collection of similar items by the same author. The review of this collection may be found at Graphics for the Calculus Classroom.
Type of Material:
JAVA applets, with a short introductory text.
This material would serve as a basis for supplemental homework assignments for students of calculus.
Any web browser supporting Java.
Identify Major Learning Goals:
This material can be used by an instructor to enrich a lecture or can be assigned to students for individual perusal.
It is useful at two levels. First, it may be used to enhance students' understanding of functions. The height of the bouncing ball, plotted against time, is a series of parabolas. This gives a nice and natural example of a function that analytically must be defined piece-wise. Similarly the velocity gives an example of a naturally discontinuous function.
Second, it can serve to enrich students' understanding of the relation between acceleration, velocity and displacement. The example is considerably more interesting than the usual "falling body;" determining the height function algebraically (a suggested homework assignment) is a realistic and challenging exercise.
Target Student Population:
Students in the first semester of calculus.
Prerequisite Knowledge or Skills:
Students should have experience graphing functions. For the more calculus-intensive use, students should have been introduced to first and second derivatives and their applications to linear motion.
Evaluation and Observation
The example is well chosen; the graphics are appropriately and elegantly handled. The inclusion of the clock measuring elapsed time is a very nice touch.
No features of concern. If this item were being revised, it could be enhanced by sliders controlling the height of the initial drop and the elasticity of the ball. But this would be icing on the cake.
Potential Effectiveness as a Teaching Tool
The physical and mathematical phenomena are shown clearly and efficiently.