You Send Me Swinging!

Using Parametric Equations to Model Motion

Dedra EatmonNCSSM

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:

( ) sin( ( ))

and

( ) cos( ( ))

f x A B x C D

f x A B x C D

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?