Swinging Ellipses - Plotting an Ellipse
Recommended for grades 9–12.
Introduction
Any ellipse centered at the origin can be expressed in the form
where ± a and ± b represent the x- and y-intercepts of the ellipse.
To graph an ellipse on a calculator, the expression above must first be solved for y to obtain
This equation is entered into the calculator 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 will find that the plot of velocity versus position is elliptical, and that you can model it with the standard equation of an ellipse.
Objectives
- Record position and velocity versus time data for a swinging pendulum.
- Plot data as a velocity versus position phase plot.
- Determine an ellipse that fits the phase plot.
Sensors and Equipment
This activity requires each of the following Vernier sensors and equipment (unless otherwise noted):
Additional Requirements
You may also need an interface and software for data collection. What do I need for data collection?
Download Experiment Preview
The student-version preview includes:
- Step-by-step instructions for computer-based data collection
- List of materials and equipment
Note: The experiment preview of the computer edition does not include essential teacher information, safety tips, or sample data. Instructions for Logger Pro and other software (such as LabQuest App or TI handheld software, where available) are on the CD that accompanies the book. We strongly recommend that you purchase the book before performing experiments.
Standards Correlations
See all standards correlations for Real-World Math with Vernier »
Included in the Lab Book
Vernier lab books include a CD with word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.