Northern Illinois University
Physics 150
Lab 6
Pendulum Periods
A swinging pendulum keeps a very regular beat. It is so regular, in fact, that for many years the
pendulum was the heart of clocks used in astronomical measurements at the Greenwich
Observatory.
There are at least three things you could change about a pendulum that might affect the period
(the time for one complete cycle):
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the amplitude of the pendulum swing
the length of the pendulum, measured from the center of the pendulum bob to the point of
support
the mass of the pendulum bob
To investigate the pendulum, you need to do a controlled experiment; that is, you need to make
measurements, changing only one variable at a time. Conducting controlled experiments is a
basic principle of scientific investigation.
In this experiment, you will use a Photogate capable of about 4-ms precision to measure the
period of one complete swing of a pendulum. By conducting a series of controlled experiments
with the pendulum, you can determine how each of these quantities affects the period.
Figure 1
Objectives
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Measure the period of a pendulum as a function of amplitude.
Measure the period of a pendulum as a function of length.
Measure the period of a pendulum as a function of bob mass.
Materials
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Vernier Photogate
string
two ring stands, two right angle clamps, and horizontal rod
masses totaling 300 g (including 50 g mass hanger)
meter stick
Procedure
1. Use the ring stand to hang the 200-g mass from two strings. Attach the strings to a
horizontal rod about 10 cm apart, as shown in Figure 1. This arrangement will let the
mass swing only along a line, and will prevent the mass from striking the Photogate. The
length of the pendulum is the distance from the point on the rod halfway between the
strings to the center of the mass. The pendulum length should be at least 100 cm.
2. Attach the Photogate to the second ring stand. Position it so that top of the mass is flush
with the top of the Photogate while hanging straight down.
3. Connect the Photogate to the interface.
4. Turn on the computer and start Logger Pro.
5. Logger Pro should sense the photogate.
6. Now you can perform a trial measurement of the period of your pendulum. Hold the mass
from about 10º from vertical and release. (For a pendulum that is 100 cm long, that
corresponds to pulling the bob about 15 cm to the side.) Take about 5 data points and
save your data.
Part 1: Amplitude
Determine how the period depends on amplitude. Measure the period for five different
amplitudes, using a range of amplitudes from about 10º to about 30º. Calculate the
amount that you will have to displace the pendulum each time in order to achieve the
desired amplitude angle, recording these values in the appropriate column in the Data
Table. Record the period data in the Data Table.
Part 2: Mass
Use the three masses (100 g, 200 g, and 300 g) to determine if the period is affected by
changing the mass. Measure the period of the pendulum for each mass, using an
amplitude of about 10°, and record the data in the Data Table .
Part 3: Length
Using the 200 g mass and an amplitude of 10º, vary the pendulum length in steps of 10
cm from 100 cm to 50 cm and record the period, recording the data in the Data Table. If
you have room, continue to a longer length (up to 200 cm). Remember to measure the
pendulum length from the horizontal rod to the middle of the mass.
Discussion
1. Using graph paper, plot a graph of pendulum amplitude (in degrees) vs. period T.
(Computer-generated graphs are not acceptable) Label this as "Graph #1: Amplitude vs.
Period". Scale each axis from the origin (0,0). According to your data, does the period
depend (appreciably) on amplitude? Explain.
2. Using graph paper, plot the mass vs. period, T. (Computer-generated graphs are not
acceptable) Label this as "Graph #2: Mass vs. Period". Scale each axis from the origin
(0,0). Does the period appear to depend (appreciably) on mass? Do you feel that you have
enough data to answer this conclusively?
3. Using graph paper plot a graph of pendulum length vs. period, T. (Computer-generated
graphs are not acceptable) Label this as "Graph #3: Length vs. Period". Scale each axis
from the origin (0,0). Does the period appear to depend (appreciably) on length?
4. Create two additional graphs from the data in the Table. On Graph 4, plot period squared
(T 2) vs. length (l) and label it appropriately. On graph 5, plot period (T) vs. length
squared (l2) and label it appropriately. By comparing graphs 3, 4, and 5, can you
conclude that a directly proportional relationship exists between the plotted variables?
Note that a straight line plot going through the graph's origin (0,0) is necessary for a
direct proportion.
5. Using Newton's laws, we could show that for a simple pendulum the period T is related to
the length l and free-fall acceleration g by
, or
Does one of your graphs support this relationship? Explain. (Hint: Can the term in
parentheses be treated as a constant of proportionality?)
6. From your graph of T 2vs.l, determine a value for g.
Data Table
Mass (g)
Angle (degree)
Length (cm)
Average period (s)