Crawling Around: Parametric Plots

Introduction

Imagine you are observing a bug crawling around in a figure eight path on the floor. If we define a Cartesian x, y plane on the floor, and you wished to completely describe the bug’s movements graphically, you would need to create a graph in three dimensions. This graph would need one axis to describe the x movement of the bug, another axis for its y movement, and a third axis for the time elapsed during the motion.

It is difficult to portray a graph in three dimensions on two-dimensional paper. It is relatively simple, however, to create a two-dimensional graph.

In this activity, you will model the bug’s movement by breaking the motion down into its x and y components. You can then use parametric equations to separately describe each of these components as a function of time. Finally, you will use the parametric mode in your calculator to combine these graphs and create a model that describes the motion of the bug.

Objectives

• Record the x- and y-coordinates of a rod moving in a figure-eight pattern.
• Use the recorded motion information to separately model the x- and y- motion as a function of time.
• Plot the experimental data in a y versus x graph.
• Plot the x- and y-models parametrically for comparison to the experimental data.