Activity Overview
In this activity, students use a Calculator-based Laboratory unit CBL 2™ to collect motion data as a paper plate attached to a loose spring oscillates up and down above a motion detector. They also find an appropriate mathematical model for the resulting data set.

Before the Activity

Connect the Voyage 200 to the CBL 2 with the Unit-to-Unit cable
Connect the CBR 2 via the DIG/SONIC port to the CBL 2 unit
Download DataMate for TI-73 Explorer DataMate for TI-83+ DataMate for TI-84+ application to collect data
Attach the paper plate to the end of a standard mass hanger and then attach the hanger to the spring
See the attached PDF file for detailed instructions for this activity Print pages 87 - 88 from the attached PDF file for your class

During the Activity
Distribute the pages to the class.
Follow the Activity procedures:

Zero the motion detector for the zero reference position to be equilibrium position of the plate
Position the spring plate assembly at least one meter above the detector
Pull the plate downward about 10cm and allow it to oscillate up and down and collect distance versus time data
View the distance graph
Observe that the modified period motion graph centered on the x-axis shows amplitudes that decrease with time
Use a simple sinusoidal function to model the data
Find the first maximum distance value (amplitude) and time for the first maximum to occur
Calculate the period of oscillation and number of oscillation made by the plate during the natural period of cosine function
Determine how well the modeling fits the data
Use the calculator and the motion versus time graph to find the coordinates of maximums
Find the exponential equation that best fits the distance maximums data
Determine how well the equation fits the data
Observe the original modeling equation provided a poor fit
Observe that the model in which the amplitudes decay exponentially fits the distance versus time data well

After the Activity
Review student results:

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