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Pendulum Motion II
Purpose
To discover how the period of a simple pendulum depends on the amplitude of vibration
Procedure
A simple pendulum consisting of a mass at the end of a long rod has been videotaped, and the
images have been digitized for analysis with the computer. Experimental data will be collected for 5 - 6
different amplitudes, and the period will be determined for each of these motions.
Step 1
Start Excel. When you see the blank spreadsheet on the screen, minimize it for future use.
(The video analysis tool we’ll be using sometimes becomes corrupted if Excel isn’t started first.) Start
the VideoPoint program by double clicking on its icon. When the title screen appears, click on the
Close button ( ) in the upper right corner to dismiss it. Click once on the Open New Movie button and
go to the WPMOVIES directory. From the Pendula subdirectory, open the movie assigned to your
group. Write the name of the movie here:
Movie Name ____________________
When the movie has been loaded, make sure the opening screen indicates that one object is to be
tracked. Click on OK to continue. When the main screen appears showing the movie window plus some
data windows, click on the Movie item in the menu bar and choose the option for Fill Screen from the
list of choices.
Step 2
Next we must calibrate the length measurements to be made. The pendulum in the sequence of
images is 66 cm long, and this information must be given to VideoPoint. Click on the ruler icon from the
toolbar along the left side of the screen. (The ruler is the single icon just below the up and down arrows
in the toolbar.) When the Scale Movie window opens, double click in the box next to “Known length” and
replace 1.00 with .66. (The units should be left as m.) Press Enter or click on the Continue button to
go on. When prompted to “Click on one end of the object of known length”, center the crosshair cursor
on the pivot point of the pendulum and click once. When prompted to “Click on the other end...”, center
the crosshair cursor on the black dot on the mass at the bottom of the pendulum and click once. This
black dot will be tracked during the motion. When you have marked each end of the pendulum, a line
marked “Scale 1” will appear.
Step 3
Before actually taking data, predict how you think the period will change as the amplitude of the
pendulum is increased.
Prediction _________________________________________
Step 4
Now begin taking data. To mark each point, center the crosshair cursor on the black dot on the
mass at the end of the pendulum and click once. The coordinates of the crosshair will be recorded and
the movie will automatically advance to the next frame. Since the camcorder used to make the tape
runs at 30 frames per second, you are creating a record of the pendulum’s x and y coordinates at time
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 Stephen Luzader
intervals of 1/30 sec. The cursor should already be on the black dot because of the calibration just
carried out. Carefully position the cursor in each frame until you have marked the dot in all the frames of
your movie. When you have marked the dot in the last frame, a red label will appear and the movie will
stop advancing. As a check, write down the name of your movie and the total number of frames
measured:
Movie Name:
____________________
Number of frames:
__________
Step 5
Plot a graph of the horizontal coordinate (x) vs time. Click on the Graph icon in the toolbar (the
last of the group of four icons just below the ruler icon--the one that looks like a graph). When the Graph
Setup window appears, choose Time for the Horizontal Axis and Point S1(X) for the Vertical Axis and
then click on the Plot button to see the graph. Use the mouse cursor to drag the borders of the graph out
to enlarge the graph window to fill a large part of the screen. Then go to the File menu and choose
Print... to print a copy of your graph. This is to be included with your final report.
Step 6
Close the Graph window and click on the Table icon just above the Graph icon in the toolbar.
You’ll determine the period by finding the time interval between alternate minima of the horizontal
position. Use the scroll button to scan through the data and record the x coordinates and times for three
successive extrema in the x column:
X value of first minimum
__________
Time
__________
X value of first maximum
__________
Time
__________
X value of second minimum
__________
Time
__________
(Did you remember to include units?)
Step 7
Now calculate the amplitude of the position variation, which is half the distance between the first
maximum and the average values of the first and second minima (show your work):
Amplitude =
__________
Step 8
Find the amplitude of the angular vibration of the pendulum in radians. You must show a
derivation of how to extract this from the length of the pendulum given in Step 2 and the amplitude of
the variation of the x coordinate just found in Step 7.
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 Stephen Luzader
Angular Amplitude =
___________
Step 9
Calculate the period of the vibration, which is the time interval between the first and second
minima (show your work):
Period =
__________
Step 10
Summarize the data for the class.
Amplitude (rad)
Period (sec)
____________
___________
____________
___________
____________
___________
____________
___________
____________
___________
____________
___________
Step 11
Summarize the results. Do the experimental results agree with your original prediction? How
can we test any theoretical prediction about how period depends on length? How do the experimental
results compare with the prediction?
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 Stephen Luzader