Physical Science
1.1 Sound & Vibration
Presearch SV2: The Simple Pendulum
“Science gains from the pendulum more than one can expect. Already the
regularity of its motion promises the most conclusive results.”
- Jean-Bernard-Leon Foucault, 1851
“It don’t mean a thing if it ain’t got that swing. Doo wop, doo wop.”
- Irving Mills, 1931
Themes: Cause & Effect, Cycles
Objectives:
1) Identify the qualities of a pendulum that affect its frequency.
2) Use a pendulum to demonstrate the principles of frequency,
period, and amplitude.
3) Distinguish between potential and kinetic energies in the motion of
a pendulum.
Primary Questions:
1) What effect does a pendulum’s length have on its frequency?
2) What effect does the weight of a pendulum’s bob have on its
frequency?
3) What effect does a pendulum’s amplitude have on its frequency?
4) What specific relation exists between a pendulum’s frequency and
its period?
5) How do potential and kinetic energies differ?
Investigation:
____ Investigation SV2:The Simple Pendulum
(attached)
Writing:
____ Lab report: The Simple Pendulum
(attached)
Vocabulary:
____ Add the following to your Academic Vocabulary. Define each as it
applies to the subject of pendulums.
frequency
amplitude
period
hertz
harmonic motion
oscillation
Who’s Who:
____ Identify each of the following, and briefly describe their contributions
to the study of pendulums:
Galileo Galilei
Jean-Bernard-Leon Foucault
Physical Science
1.1 Sound & Vibration
Investigation SV2: The Simple Pendulum
Introduction:
Recently, you conducted an investigation using a monochord to
study sound and vibration. In the present investigation you’ll deepen your
understanding of vibration by observing a pendulum. A pendulum consists
of a weight, or bob, suspended on a string or wire in such a way that it can
swing freely back and forth from a pivot point. One advantage to using a
pendulum is that its vibrations are slow enough to observe and measure.
Some of the earliest studies of pendulums were undertaken in the
seventeenth century by Galileo Galilei. It’s believed that his interest was
sparked by watching the swing of a chandelier in the Pisa Cathedral. In this
investigation, you’ll conduct your own exploration to see what you can
discover about the nature of pendulums and vibration. In particular, you’ll
examine how the behavior of a pendulum is affected by three variables: the
amplitude of the pendulum, the weight of its bob, and the pendulum’s
length.
Materials:
You’ll need the following to conduct this investigation:
- a pendulum (string, paperclip, metal washers as provided)
- metric rule, in cm.
- timer (a clock or watch will do)
- calculator
- paper, pencil as needed.
Procedure:
You’ll work with a partner for this investigation, according to the
instructions that follow. Be thoughtful and thorough in your work, and
keep your own records and data. You’ll be asked to compose a written
report of findings when finished.
Part I: Frequency and Amplitude
1) To begin, construct a pendulum with the materials provided. Your
pendulum will consist of a length of string with a paperclip tied to one end.
The paperclip will be bent into a hook so that a few metal washers can be
attached to form a bob. An example will be shown in class.
Next, you’ll need to suspend the pendulum securely from a table or
doorway so that it can swing freely.
You’ll also need to measure the pendulum’s length accurately. The
measurement must be made from the point of suspension to the center of
the bob. This is an important measurement, so do it carefully to the nearest
half-centimeter.
2) Determine the frequency (f) of your pendulum. Frequency is
expressed in Hertz (Hz), which is the number of cycles (c) your pendulum
completes in one second. A cycle, or oscillation, consists of one swing of the
pendulum out and back. You can find the frequency for your pendulum by
counting the number of cycles it completes in a minute, and dividing this
number by 60. You and your partner will need to divide your labors so that
one of you is counting cycles of the pendulum while the other watches a
timer. In this fashion, perform at least five trials of your pendulum, using
the same number of washers and the same length pendulum, and record
the data for each trial into a table. You’ll also want to find an average for
your trials. Your data table might look something like this:
length of pendulum: ________ cm.
trial #
cycles per minute (c) Hertz (Hz) = (c)/60
1
2
3
4
5
average:
3) Your last task for this part of the investigation is to compose a
response to the following prompt:
Q1: A pendulum’s amplitude (a) is the distance it moves from center,
either at the start of a trial or during the trial itself. What effect does a
change in amplitude have on the frequency of your pendulum? Explain
how this can be demonstrated and conduct a test. Record your data and
findings.
Part II: Frequency and Weight
Before conducting this part of the investigation, compose and record
responses to the following prompts:
Q2: How do you think doubling the weight (w) of the bob will affect
your pendulum’s frequency? Explain your reasoning.
Q3: How do you think tripling the weight (w) of the bob will affect
your pendulum’s frequency? Explain your reasoning.
Q4: How do you think halving the weight (w) of the bob will affect
your pendulum’s frequency? Explain your reasoning.
Q5: In general, what effect do you think weight of the bob has on the
behavior of a pendulum? Explain your reasoning.
4) Now conduct an experiment to test your responses to the prompts
above. As before, perform at least 5 trials for each weight, and record your
data in tables. Each of your tables might look like this:
bob weight (in washers): ________
trial #
cycles per minute (c) Hertz (Hz)
1
2
3
4
5
average:
Q6: Look over your data. How do your results compare to your
predictions? What conclusions can you draw from this part of the
investigation?
Part III: Frequency and Length
Before conducting this part of the investigation, compose and record
responses to the following prompts:
Q7: How do you think doubling the length (l) of the pendulum will
affect its frequency? Explain your reasoning.
Q8: How do you think tripling the length (l) of the pendulum will
affect its frequency? Explain your reasoning.
Q9: How do you think halving the length (l) of the pendulum will
affect its frequency? Explain your reasoning.
Q10: In general, what effect do you think the length of a pendulum
has on its behavior? Explain your reasoning.
5) Now conduct an experiment to test your responses to the prompts
above. Do not change the weight of the bob for this part of the
investigation. As before, perform at least 5 trials for each length, and
record your data in tables. Each of your tables might look like this:
pendulum length: ________
trial #
cycles per minute (c)
Hertz (Hz)
1
2
3
4
5
average:
Q11: Look over your data. How do your results compare to your
predictions? What conclusions can you draw from this part of the
investigation?
6) Your next task is to compose a graph on grid paper showing the
relation between length of a pendulum and its frequency. Your graph will
need an x-axis for plotting the length of a pendulum (in cm.), and a y-axis
for plotting the frequency of a pendulum (in Hz).
Part IV: Length and Period
The period (p) of a pendulum describes the amount of time needed
for the pendulum to complete one full cycle or oscillation. This part of the
investigation will guide you in finding the period for your pendulum.
7) Determine the time in seconds (s) needed for your pendulum to
complete 10 cycles. As before, you and your partner will have to work
together closely in the collection of data. Conduct 5 trials for your
pendulum, without changing the pendulum’s length or the weight of its
bob. Record your data in a table like this one:
pendulum length: ________
trial #
time for 10 cycles (s) period (p) = (s)/10
1
2
3
4
5
average:
8) Repeat step 7 for 4 other lengths of your pendulum, and record
your responses in similar data tables. In each case, keep the weight of the
bob the same.
9) Now graph the averages from the period tables against the lengths
of the pendulums you tested in steps 7 & 8 above. Using grid paper,
construct an x-axis for the lengths of the pendulums, and a y-axis for the
periods of the pendulums. The scales needed for these axes will depend
upon the numbers found in your data tables.
Analysis and Reflection:
Recall that the purpose of this investigation was to see how a
pendulum’s behavior is affected by changes in its length, its amplitude,
and the weight of its bob. To aid in your analysis, compose written
responses to the following prompts:
a) How is a pendulum’s frequency affected by changes in its
amplitude?
b) How is a pendulum’s frequency affected by changes in the
weight of its bob?
c) How is a pendulum’s frequency affected by changes in its
length?
d) How would you describe the relation between a pendulum’s length
and its frequency?
e) How would you describe the relation between a pendulum’s length
and its period?
And last, consider this question with a thoughtful response:
f) What has this investigation added to your understanding of
vibration? In particular, what connections can you draw between
this investigation and previous work with the monochord?
Physical Science
1.1 Sound & Vibration
Lab Report SV2: The Simple Pendulum
Recently you conducted an investigation into vibration using a
pendulum. In this assignment, you will compose a written report of your
investigation.
Your report must include the following elements:
1) An introduction. Orient your reader to the investigation by
providing relevant background information, and a statement of
the investigation’s purpose. Include any predictions or hypotheses
you posed during the investigation.
2) An annotated diagram showing the construction of a pendulum.
Include a list of materials.
3) A list of steps or procedures used in conducting the investigation.
Incorporate text and diagram as needed.
4) Tables of data collected during the investigation. Be sure to
include titles and annotation as necessary.
5) A discussion of findings and conclusions. What did you notice?
What did you discover? How did your results compare to the
hypotheses you posed? What new questions arose for further
investigation?
6) A list of technical terms necessary to the investigation, as well as
their definitions.
Attach your finished product to this cover for turn-in.