Activity Detail
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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
  • 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

    		Other Downloads




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    Subject Area:
    Math : Calculus : Other Functions

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    60 Minutes

    Device:
    TI-92 Plus / Voyage™ 200

    Apps:
    DataMate

    Software:
     

    Accessories:
    CBL™/CBL 2™, CBR™/CBR 2™, Unit-to-Unit link cables

    Other:
    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


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