Education Technology

Modeling Damped Motion

Published on 06/09/2008

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