You Send Me Swinging! Using Parametric Equations to Model Motion Dedra Eatmon NCSSM TCM Conference 2007

The “Swing Lab” is an activity used to demonstrate an application for trigonometric functions used in parametric mode for modeling Student can apply what they have learned and have fun, also

Prior Knowledge Familiarity with parametric mode on calculator Knowledge of sine and cosine functions and what each parameter represents in:

To gather the necessary data for the lab collection students will need:  Tape measures and/or meter/yard sticks  Stopwatches

Swinging Objectives By the conclusion of this lab activity, your students will be able to  Collect data to accurately represent amplitude, vertical shift,and period of swinger  Use knowledge of trignometric functions to represent the path  Effectively communicate data collection procedure, solutions, and results through written report

The Line Up Students will work in 3-4 person groups  Student 1 will be the swinger  Student 2 will measure vertical distance  Student 3 will measure horizontal distance  Student 4 will be the timekeeper In groups with 3 students, someone will measure distance and keep time

Procedure The students will have to take measurements before and while the swinger is in motion Before  Height of the swinger at equilibrium

Data Collection During  Height of the swinger at their highest point above the ground  Horizontal distance from equilibrium to the swinger’s highest positon above the ground  The length of time to complete five swing cycles What is a cycle? Talk to students about any difference between vertical and horizontal cycles.

Let’s Swing In groups of 3 or 4, we will swing... not really... but we can act like it. You will need:  A pendulum  One or two meter sticks  A stopwatch

Finding the Values How do we calculate the coeffiencents and shifts for the parametric equations?