# Activities

• • • ##### Subject Area

• Math: Calculus: Transcendental Functions

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-92 Plus / Voyage™ 200

CBL™/CBL 2™
CBR™/CBR 2™

• ##### Other Materials
This is Activity 11 from the EXPLORATIONS Book:
Discovering Math on the Voyage 200.

The following materials are required for this activity:
• Light spring
• 1 standard slotted mass hanger
• 1 paper plate

## Modeling Damped Motion

#### 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
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.

• 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