IIT/FIELD MUSEUM – High School Transformation Project
Lesson: Pendulum Lab
Conceptual Physics, Hewitt
Unit 1, Chapter 25 Vibrations and Waves
Section 25.1
Guiding Questions:
1. What are the factors that affect the period of a pendulum?
2. What is the relationship between those factors?
Context of Lesson
This lesson should come after an introduction to mechanics, so that students already have concepts of
speed, time, and velocity. This lesson also is an opportunity for students to work on a technological design
within parameters, and to identify and isolate relevant variables. They will have a chance to see that
inquiry procedures are guided by the question asked, and that there is not a single correct way to proceed,
but many ways that can achieve the desired aim.
Main Goals/ Objectives:
By the end of this lesson, students will be able to:
 Build a pendulum that has a period of 2s
 Identify which variables affect the period of the pendulum, and which do not.
 Compare their experimental results to the small angle pendulum equation.
 Explain that scientific knowledge should be based on empirical data.
 Explain that inquiry procedures are guided by the question asked, and
 Explain that all scientists performing the same procedures may not get the same results.
Nature of Science: Integrated Theme
 Distinguish observations from inferences, explain that inferences should be based on observations,
and explain that the development of scientific knowledge involves both observations and
inferences so scientific knowledge is partially inferential.
 Explain that scientific knowledge should be based on empirical data.
Scientific Inquiry: Integrated Theme
 Explain that scientific investigations all begin with a question, but do not necessarily test a
hypothesis
 Explain that there is no single scientific method and provide at least two different methods
 Explain that inquiry procedures are guided by the question asked
 Explain that research conclusions must be consistent with the data collected
General Alignment to Standards
State Goal 11A: Know and apply the concepts, principles, and processes of scientific inquiry.
11.A.4a – Formulate hypothesis referencing prior research and knowledge.
11.A.4b – Conduct controlled experiments or simulations to test hypotheses.
State Goal 11B: Know and apply the concepts, principles, and processes of technological design.
11.B.4b - Propose and compare different solution designs to the design
problem based upon
given constraints including available tools, materials, and time.
State Goal 12D: Know and apply concepts that describe force and motion and the principles that
explain them.
12.D.4a – Explain and predict motions in inertial and accelerated frames of reference.
PSAE STANDARD 11A – SCIENTIFIC INQUIRY

11.11.01 Understand and follow procedures relating to scientific investigations, including
understanding the design and procedures used to test a hypothesis, organizing and analyzing data
accurately and precisely, producing and interpreting data tables and graphs, performing appropriate

calculations, applying basic statistical methods to the data, identifying appropriate conclusions,
making predictions, and evaluating competing models.
12.11.79 Understand the types of motion such as linear, circular, parabolic, and periodic. Explain and
predict motions in inertial and accelerated frames of reference.
Materials:
 ring stand
 pendulum clamp
 string
 1” diameter pendulum bobs, or assorted weights of similar size
 scissors
 stop watch
The Lesson:
This lesson is intended for two class periods. One day one, the students will investigate the factors that
affect the period of a pendulum, and on day two will describe the relationship between period and length.
The relationship between the period of a pendulum and its related factors can be expressed
____
T = 2π√(L/g)
Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
This exercise will have an inquiry component, as the day 1 lesson relies in part on the naïveté of the
students. They should explore the effect of changing the mass or angle on the period, because they don’t
know any better. As they record the effect of changing different variables, the students discover for
themselves that the period depends on length and length alone. They then use this knowledge to devise a
pendulum to have a period of exactly 1 second by varying the length.
To successfully integrate inquiry into the activity, the process of discovery is quite important during the
day 1 lesson. The students must be made aware that success is most effectively achieved if all of the
variables are explored, but only one variable is considered at a time. They can be notified of this critical
aspect before the activity begins, but they will inevitably need reminding as you monitor their progress
during data collection.
The students should be investigating all possible factors on Day 1, so do not lead them to believe that
length is the only factor worth considering. As they progress with the data collection, they will be led by
their own interpretation of the data, which will in turn indicate their method to construct a 1-s pendulum,
which is of course to increase the length to increase the period, or to decrease the length to decrease the
period, as the case might be.
The day 2 activity focuses on refining the relationship between the length and the period of their
pendulum. The students will construct a data table and a best fit graph. The students should be made
aware of the possible curved relationship of the data. They should be instructed not to construct a
“connect the dots” graph, but that they must sketch a smooth curve to express the period as a function of
length.
Day 1
Bell Ringer
Reference students’ prior knowledge about pendulums, and guide the discussion towards thinking about the
method that they will use in their investigation. Ask the students. We’re going to do an investigation of a
pendulum today, but before we start...”




Has anyone ever seen a grandfather clock?
Has anyone seen the BIG pendulum at the Museum of Science and Industry?
What are the possible factors that could affect the period of the pendulum?
Why would you test only one factor at a time?


If you were timing an event that lasted about 1 second with a stopwatch, could the accuracy be
lower than you would want?
Would timing a series of 10 periods yield more accurate results than timing a single period?
Instructions:
Tell the class that a simple pendulum consists of a small heavy ball (the bob) suspended by a lightweight
string from a rigid support. The bob is free to oscillate (swing back and forth) in any direction. A pendulum
completes one cycle or oscillation when it swings forth from a position of maximum deflection and then
back to that position. The time it takes to complete one cycle is called its period.
Tell the class that they will be working in groups to build a 1s pendulum. They should proceed based on the
factors that were discussed during the bell ringer. Each group will need to select some supplies as well.
Give the students instructions on supplies based on what will work well in your classroom. When they have
a 1s pendulum, they can call you over to demonstrate it. A successful demonstration will get initialed, and
earn them credit towards the assignment.
Homework
Hewitt, Ch 25
Check concepts 1-7
Assessment:
The most critical assessment for Day 1 is monitoring the groups as they work. Some groups may start with
length, others with mass. Encourage all groups to vary length and mass at least once. Also be sure to point
out the problems with changing multiple variables at the same time.
Day 2
Bell ringer:
Reference the students’ observations from Day 1 regarding the effect of changing mass, angle, and length
on the period of their pendulum. Describe the finished product for the lesson, which will be a graph of the
relationship between period and length of a pendulum.
Instructions:
Step 1: Set up a pendulum using the listed equipment. Make its length 65 cm. Measure its period three
times by timing the oscillations with the stopwatch or the computer system. Record the data on the Day 2
data sheet.
Step 2: Shorten the pendulum length by 5 cm. Measure its period as in Step 1, and record the average
period on the Day 2 data sheet.
Step 3: Complete Day 2 data sheet for the remaining pendulum lengths indicated there. Measure periods
as you did in Step 1.
Step 4: Make a graph of the period (vertical axis) vs. the length of the pendulum (horizontal axis).
Modifications/Accommodations:
Students with IEP’s can be given extra time to complete the activity. In addition, students for whom extra
assistance is indicated can be given individualized instruction. The teacher should take care to lead the
students to obtain the desired results without simply giving the answers, as the inquiry component can
access the varying learning styles of students with IEP’s.
Attachments:
Data sheet day 1 and day 2
Assessments for data sheets
Name:_______________________________________per:__________date:________________________
Pendulum Lab Data sheet – Day 1
trial
length
mass
angle
Time / 10 cycles
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
1. Briefly describe the method you used to construct your pendulum.
2. What was the mass of your pendulum?
3. What effect, if any, does mass have on the period of a pendulum?
period
4. What effect, if any, does amplitude (size of swing) have on the period of a pendulum?
5. What was the length of your pendulum?
6. What effect, if any, does length have on the period of a pendulum?
7. If you set up your pendulum where there was less gravity, would the period be less than, the same as, or
greater than it would be in your lab?
Name:_____________________________________per:___________date:__________________
Pendulum lab – day 2 data sheet
Length
Trial 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Trial 2
Trial 3
Avg.
period
1. Describe your graph. Is it a straight line that shows that the period is directly proportional to the length?
Or is it a curve that shows that the relationship between period and length is not a direct proportion?
2. From your graph, predict what length of pendulum has a period of exactly two seconds.
predicted length = ____________
3. Measure the length of the pendulum that gives a period of 2.0 s.
measured length = ____________
4. Compute the percentage difference between the measured length and the predicted length.
Name:_______________________________________per:__________date:________________________
Pendulum Lab Data sheet – Day 1
Students should change only one variable at a time; more tables may be needed as necessary.
trial
length
mass
angle
Time / 10 cycles
period
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
1. Briefly describe the method you used to construct your pendulum.
Answers will vary; one possible response is: One variable at a time was manipulated until it was
discovered that changing the length is the only variable that matters. The length was changed until the
period was recorded to be exactly one second.
2. What was the mass of your pendulum?
Answers will vary; masses between 5-g and 100-g work well with common polyester sewing thread.
3. What effect, if any, does mass have on the period of a pendulum?
Mass has little to no effect on the period of a pendulum, just as mass does not effect the rate of a freely
falling object if air resistance is neglected.
4. What effect, if any, does amplitude (size of swing) have on the period of a pendulum?
Changing the amplitude has little to no effect for angles between 0o and 30o. For large angles, the bob
will seem to “bounce” and is not really simple harmonic motion when this happens.
5. What was the length of your pendulum?
Note: mathematical solutions are given for your reference,
and do not need to be required for successful completion of this activity.
Solving T = 2π√(L/g) for L yields L = gT2/42.
For T = 1 s, L = 24.8 cm. A length of 24, 25, or 26 cm is considered acceptable.
6. What effect, if any, does length have on the period of a pendulum?
As the length is increased, the period is increased.
7. If you set up your pendulum where there was less gravity, would the period be less than, the same as, or
greater than it would be in your lab?
If gravity were decreased, the pendulum would move slower and therefore have a greater period. The
period is inversely related to the acceleration due to gravity.
Name:______________key____________per:___________date:__________________
Pendulum lab – day 2 data sheet
Students should collect as much data as time allows; it is helpful but not essential to take enough data to
fill the table. The graph should have a title and its axes labeled, including units. The period depends on
the length, so length would ideally be put on the x-axis; however, this is not critical.
Length
Trial 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Trial 2
Trial 3
Avg.
period
1. Describe your graph. Is it a straight line that shows that the period is directly proportional to the length?
Or is it a curve that shows that the relationship between period and length is not a direct proportion?
A curved relationship should be evident.
2. From your graph, predict what length of pendulum has a period of exactly two seconds.
Predicted length = ____________
L = gT2/42. For T = 2s, L = 99.3 cm.
Results will vary; students should be encouraged to sketch a smooth curve based on their data to give a
reasonable extrapolation.
3. Measure the length of the pendulum that gives a period of 2.0 s.
Measured length = ____________
If time permits, students should construct a pendulum with a length of 2s.
4. Compute the percentage difference between the measured length and the predicted length.
% difference = (predicted - measured) / measured * 100