Name:
Partner’s name:
Discovery Lab
Pendulums
When a mass suspended from a string is raised and released it oscillates. The oscillating motion
of a simple pendulum has been used throughout history to record the passage of time.
OBJECTIVES
• Determine the factors that influence the
time interval required for a pendulum to
complete one full swing (period T).
• Investigate the nature of pendulum.
Procedure
MATERIALS
metal washers
string, ~1.00 m
masking tape
meterstick
paper clip
protractor
stopwatch
stick
1. Tape the stick to the table.
2. Construct a pendulum like the one shown. Tie a bent paper clip to
one end of a 1.05 m cord. Tie the other end of the string to the string so that the bottom of the
paper clip hangs about 1.0 m below the stick. Hang 2-3 small metal washers from the paper clip.
Bend the paper clip to hold the washers securely.
3. Tape the protractor to the edge of a table as shown. The string should fall across the center of
the protractor.
4. Allow the pendulum to hang undisturbed. This vertical position is its resting or equilibrium
position labeled B in the picture. Then pull the washers to one side so that the string is at the
specified angle (see below!) from vertical. Release the washer and simultaneously start the
stopwatch.
5. Record the time required for the pendulum to complete ten oscillations. Note that one
oscillation is a back-and-forth swing from the displaced position A to C and back to A.
You will need to test several different combinations of angle, number of washers, and string length
in order to determine how each of these factors influence period of the pendulum. You must test
each combination 3 times and calculate the average period for each.
6. Record the time for the pendulum to complete ten oscillations for each of the following
conditions. Test each set of conditions 3 times and record the average period.
Angle from vertical
8
6
4
8
6
4
8
6
4
6
6
6
6
6
Number of Washers
3
3
3
6
6
6
9
9
9
3
3
3
3
3
String length (m)
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
0.80
0.65
0.55
0.45
0.30
BE SURE THAT YOU AVERAGE THE PERIOD EVERY
TIME
Be sure to use the correct number of significant
digits and the appropriate SI uits
2
Analysis
A. Watch the oscillation of a pendulum carefully. Sketch the forces on the bob when the pendulum is at its
maximum angular displacement and at zero displacement (at equilibrium position).
B. Explain why the pendulum oscillates back and forth, using your knowledge of force and motion.
C. Which of the factors that you measured might affect period? Explain.
D. Select the appropriate data to make each of the graphs listed below. You will NOT include all data in
each graph. Think carefully about what data to graph and be sure that you are varying only one factor at a
time.
1) Make a graph of period versus angle. What can you conclude?
2) Make a graph of period versus mass. What can you conclude?
3) Make a graph of period versus length. What type of the graph is it? What can you conclude?
How does the period depend on length?
4) Make a graph of period versus (length)1/2. Draw the best fit line. Equation of your best fit
line can be written as T  m L , where T is period and L is length of the pendulum and m is the slope of
the line. Find m.
ALL GRAPHS MUST BE COMPUTER GENERATED OR ON GRAPH PAPER. AXES SHOULD BE
FULLY LABELED. ERROR BARS SHOWING THE UNCERTAINTY IN T SHOULD BE INCLUDED.
DO NOT ‘CONNECT THE DOTS’.
E. Based on your graphs and results above, determine the length of the pendulum that takes 1.0 s to
complete one full swing (T = 1 s)
F. Would adding mass to the pendulum change the time required for one full swing?
G. To make a pendulum that requires 2.0 s for one full swing, would you lengthen or shorten the cord?
Explain your reasoning.
Number of
washers
Angle
Length of
pendulum
Period, T (seconds)
Trial 1
Trial 2
Trial 3
Average
Uncertainty
% Error
3
Number of
washers
Angle Length of
pendulum
Period, T (seconds)
Trial 1
Add as many rows as you need it.
Trial 2
Trial 3
Average
Uncertainty
% Error