Damped Harmonic Motion in action

  1. Set up a Rotary Motion Sensor (RMS) on a pole clamped to your table.
  2. Connect the RMS to the LabPro interface, and connect the interface to your computer.
  3. Pick a meterstick with holes in it. Measure the mass and all dimensions of the meterstick.
  4. Compute the moment of inertia I of your meterstick in units of (kg*m^2).
  5. Attach the meterstick to the RMS so that it rotates around a point h = 30 cm from the center of the meterstick.
  6. Download this LabPro file to your desktop
  7. Double-click on the file you have just downloaded ... you should see LabPro start and show you a screen with several panels.
  8. Choose Experiment -> Set Up Sensors -> LabPro1 and pick the "DIG/SONIC1 Rotary Motion" sensor. Right-click and make sure that "Reset (zero) on Collect" is NOT checked.
  9. With meterstick hanging down and motionless, zero the sensor
  10. Start collecting data, then have someone gently move the meterstick about 20 degrees to the side and release it. Collect data for 100 seconds.
  11. What is the MEASURED angular frequency omega of your meterstick? (Hint: count the number of oscillations it makes over 20 or 30 seconds, and use the period to compute omega)
  12. What is the theoretical angular frequency of the meterstick if you assume that there is no air resistance? (Hint: write a formula relating angular acceleration to angular displacement, then express the angular acceleration in terms of torque and moment of inertia; or see your textbook). How does it compare to the actual frequency?
  13. Use the "Analyze -> Curve Fit" command to fit a negative exponential function to THE UPPER ENVELOPE of your measurements as a function of time.
  14. Write down an equation of the form 
                                    -t/tau
          max theta (t)  =  A  e          +  0
    What is the value of A? What does it represent? What is the value of tau? What does it represent?

    15. If you have time ...

  15. Attach a paper sail to the edge of your meterstick so that its cross-section area for air resistance is twice as large as the bare meterstick. What SHOULD this do to the decay time of the meterstick? Be quantitative here ....
  16. Repeat the experiment with the sail attached. What is the value of the time constant now? Does the change in its value agree with your prediction?
  17. Modify the "Rotational Kinetic Energy" column by replacing the bogus value for moment of inertia I by your actual value, in units of (kg*m^2). Measure the time constant tau(E) of the ENERGY of the meterstick.
  18. How does the time constant of the amplitude compare to the time constant of the energy? Can you explain the relationship theoretically?