Swinging Ellipses - Plotting an Ellipse > Experiment #21 from Real-World Math with Computers

Figure from experiment 21 from Real-World Math with Computers

Introduction

Any ellipse centered at the origin can be expressed in the form

$\frac{{{x^2}}} {{{a^2}}} + \frac{{{y^2}}} {{{b^2}}} = 1$

where ± a and ± b represent the x- and y-intercepts of the ellipse.

To graph an ellipse on Logger Pro, the expression above must first be solved for y to obtain

$y = \pm b\sqrt {1 - \frac{{{x^2}}} {{{a^2}}}}$

This equation is entered into the computer in two parts, one expression for the positive part (upper half of the ellipse) and one for the negative part (lower half of the ellipse).

In this activity you will use the Motion Detector to record the position and velocity of a swinging pendulum. You’ll find that the plot of velocity vs. position is elliptical, and that you can model it with the standard equation of an ellipse.