LAB
IV. THE PENDULUM
Problem:
What is the relationship between the length of a pendulum
and its period?
NOTE: DO
NOT BEGIN THE EXPERIMENT UNTIL EACH PERSON IN YOUR GROUP HAS READ
THE BACKGROUND AND ANSWERED THE BACKGROUND QUESTIONS.
Background
and Inquiry: A simple pendulum consists of a weight, called
a bob attached to the end of a string fixed at the other end.
The pendulum has been used since the 16th century to measure time.
The famous scientist Galileo was the first to observe its properties.
Today you will repeat some of Galileo first experiments.
Begin by observing
the swing of the bob. Without doing actual measurements observe
the general properties of the pendulum by observing the motion
of the bob (e.g., change the length of the string and change the
direction the bob swings). If you have additional masses, change
the mass and observe what happens. Discuss with your group what
are the general properties that you have observed.
Today you
will change the length of the string and observe the time it takes
for the bob to swing back and forth. What kind of change do you
expect to observe? For example: Would you expect if you double
the length it will take twice as long to swing? If you double
the mass would the bob swing twice as fast? What type of mathematical
relationship do you expect to observe? Justify your statement!
Background
Questions:
1) What is a pendulum?
2) What scientist first observed the properties of a pendulum?
What are some properties he may have observed?
3) Would you expect if you double the length it will take twice
as long to swing?
Hypothesis:
State your hypothesis. Justify your statement!
Materials:
string, meter stick, two 20 g. masses, digital stopwatch,
ring stand
Procedure:
1) Copy table
I and table II into your lab notebook.
2) Add a 20 gm. mass to the end of the string. Set the length
of the string to 20 cm.
Diagram:
NOTE: The
period (T) of a pendulum is the time it takes for a mass (called
a bob) to swing back and forth once. Since the time for this event
may be too quick to measure, it will be necessary to calculate
an average value. ExampleLet the weight swing back and forth
two times or 2 periods. Divide the time in seconds you measured
by 2. This will give you a more accurate value for the period
of the pendulum (T).
2) Record the period of a pendulum for six different lengths (20,
40, 60, 80, 100 and 120cm.) of string using the 10 gm. weight.
Remember to repeat each measure several times, taking an average.
Record your results in Table I shown below.
3) Repeat using 40 gm. of mass.
Record your
results in Table II.
Results:
Complete the following table.
TABLE I:
Mass of bob = 20 GMs. Length, L (cm.) Two Periods (2T)
(sec) One Period (T)
NOTE: ONE
PERIOD IS ONE SWING BACK AND FORTH! MEASURE TWO PERIODS IN THIS
LAB, THEN DIVIDE BY TWO TO GET THE ONE PERIOD DATA. DO NOT MEASURE
ONE PERIOD WITH THE STOPWATCH.
Length 
Two Periods
(Student I) 
Two Periods
(Student II) 
Average 
One Period (T) sec. (half of average) 
20 cm. 




40 cm. 




60 cm. 




80 cm. 




100 cm. 




120 cm. 




TABLE II;
Mass of bob = 40 GMs.
Length 
Two Periods Student I 
Two Periods Student II 
Average 
One Period (T) sec. (half of average) 
20 cm. 




40 cm. 




60 cm. 




80 cm. 




100 cm. 




120 cm. 




Graphing
Activities:
1) Using
graph paper, label the xaxis length (L) and the yaxis period
(T). Using Table I plot your points. Do not Join the points instead
make a smooth curve using a french curve as shown in class.
Discussion:
1) Discuss the shapes of your plots.
2) Why does it not matter what the weight of the pendulum is or
where the pendulum starts it swing? Can you relate this to why
to objects that have the same mass always fall at the same rates?
3) What are the independent and dependent variables?
4) What happens to the dependent variable when the independent
variable increases? decreases?
5) What factors are held constant in each experiment?
6) What type of relationship is demonstrated in this experiment?
7) How does the relationship shown in this experiment compare
with other relationships you have so far seen?
Applications:
How could
a pendulum be used to tell time? How would you design a clock
using a pendulum?
