Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Conics

9-12

60 Minutes

• ##### Device
• TI-73 Explorer™
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

CBL™/CBL 2™
CBR™/CBR 2™
Sensor - Motion Detector
TI Connectivity Cable
Vernier LabPro®

• ##### Other Materials
This is Activity 22 from the EXPLORATIONS Book:

The following materials are required for this activity :
• Pendulum bob
• String
• Meter stick

## Swinging Ellipses: Plotting an Ellipse

#### Activity Overview

In this activity, students will use a motion detector to record the position and velocity of a swinging pendulum. They will plot the data as a velocity versus position phase plot and determine an ellipse that fits it.

#### Before the Activity

• Connect the motion detector to DIG/SONIC port of the CBL 2™ or the DIG/SONIC 1 port of the LabPro®
• Connect the CBL 2 or LabPro to the calculator using the Unit-to-Unit cable
• See the attached PDF file for detailed instructions for this activity
• Print pages 22-1 thru 22-5 from the attached Student Edition PDF file for your class
• Print pages 22-1T thru 22-3T of the Teacher Edition
• #### During the Activity

Distribute the pages to your class.

• Connect the pendulum bob to an 80 cm long string and suspend it from a support
• Arrange the Motion detector so that the bob swings back and forth in front of it and comes no closer than 50 cm.
• Examine the distance versus time and the velocity versus distance plots on the calculator
• Trace the velocity versus distance graph and record the average of the absolute values of both the x and the y intercepts in the Data Sheet
• Graph the ellipse equation
• #### After the Activity

Students' will complete the Data Collection and Analysis Sheet and answer questions listed in it.

Review student results

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary