Pendulum Lab
Go to the BPI website, find
our class, and download
the Pendulum Lab pdf file.
Raw Data: Mass
•Keep Length & Amplitude constant while
varying the Mass:
1.Set length to 1.0m.
2.Begin with amplitude of 20o
3. Use your smallest mass.
4.Record the period for 3 trials:
a.Start timing at release of mass.
b.Stop after exactly 20 periods
c. Record in your data table.
5.Repeat while adding mass
Procedure 1 - Raw Data
Amplitude
(Deg.)
20
20
20
20
20
20
20
20
20
Mass Length Period x 20
(g)
(m)
(s)
39.76
1.018
15
39.24
1.018
15
38.32
15
1.018
39.96
30
1.018
37.96
30
1.018
39.76
30
1.018
45
39.04
1.018
45
38.32
1.018
45
30.48
1.018
Raw Data: Amplitude
•Keep Length & Mass constant while
varying the Amplitude:
1.Set length to 1.0m.
2.Set an amplitude of 5o
3. Use your largest mass.
4.Record the period for 3 trials:
a.Start timing at release of mass.
b.Stop after exactly 20 periods
c. Record in your data table.
5.Repeat for angles of 10o, 15o, and 20o
You could have saved time by
using the data for 20 degrees
from Procedure 1.
Procedure 2 - Raw Data
Amplitude
(Deg.)
5
5
5
10
10
10
15
15
15
Mass Length Period x 20
(g)
(m)
(s)
38.16
45
1.018
38.88
45
1.018
35.64
45
1.018
38.68
45
1.018
38.32
45
1.018
37.80
45
1.018
38.88
45
1.018
41.40
45
1.018
40.32
45
1.018
Raw Data: Length
•Keep Amplitude & Mass constant while
varying the Length:
1.Set length to 1.0m.
2.Use an amplitude of 20o
3. Use your largest mass.
4.Record the period for 3 trials:
a.Start timing at release of mass.
b.Stop after exactly 20 periods
c. Record in your data table.
5.Repeat for lengths of 0.8m, 06m,
0.4m and 0.2m
Procedure 3 - Raw Data
Amplitude
(Deg.)
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
Mass Length Period x 20
(g)
(m)
(s)
45
1.0
39.40
45
1.0
40.12
45
1.0
40.68
45
0.8
33.92
45
0.8
33.84
45
0.8
34.00
45
0.6
29.60
45
0.6
29.32
45
0.6
29.32
23.56
45
0.4
23.92
45
0.4
24.28
45
0.4
17.08
45
0.2
16.36
45
0.2
17.80
45
0.2
Raw Data
Change the name of the sheet where
you first input your data to “Raw Data”
by right-clicking this tab and selecting
“Rename” from the popup window.
Raw Data
Format your data so that it looks like
the tables shown. The headings should
have units and be bold. All values
should be centered; limit all numbers
to two decimal places shown.
Raw Data
Change the names of three other tabs
to: Mass, Amplitude and Length. You
may need to add one or more tabs by
left-clicking here.
Null Effect of Mass
Copy/paste the Procedure 1 data set
onto the Mass sheet and compute the
averaged periods by dividing by 20. Try
using Excel to do the math…
Null Effect of Mass
After you’ve found the averaged
period, find the average of the three
trials for each mass…
Null Effect of Mass
Next, create a graph of Period vs. Mass
as shown here…
Null Effect of Amplitude
Copy/paste the Procedure 2 data set
onto the Amplitude sheet and compute
the averaged periods by dividing by 20.
Try using Excel to do the math…
Null Effect of Amplitude
Compute the averaged
period and the average of
the 3 trials for each angle.
Then create a plot of the
data, Period vs. Angle
Period vs. Length
There is a visible curve to
the data, so we are on the
right track with our
deduction. But can we
prove the equation
definitively???
Pendulum Lab – Proving the Deduced Equation:
Log Rules:
log(x )
1) x  10
2) log(mn) = log(m) + log(n)
3) log(m/n) = log(m) – log(n)
n
4) log(m ) = n · log(m)
Pendulum Lab – Proving the Deduced Equation:
We set out to prove that the period, T, of a pendulum
was given by the equation:
T C
l
g
, and that mass and amplitude have no effect on T. In
addition, we also want to determine the constant, C.
With the data we have taken, we have the information
we need to do this!
Pendulum Lab – Proving the Deduced Equation:
This equation,
T C
L
g
is the same thing as saying that,
C 0.5
T
L
g
C
T  KL , where K 
g
0.5
0.5
log T  log( KL )  log K  log L
0.5
log T  0.5 log L  log K
y

mx

b
If we plot Log T vs Log L and our deduction is correct,
then the slope of the line should be ½!!!
Period vs. Length
Pendulum Lab – Proving the Deduced Equation:
After plotting the Log T vs. Log L and fitting a line to the
curve, we now have an experimentally determined
equation that can be used to validate our deduced
expression. This equation can also be used to help us
determine the constant C. Can your team figure out
how this might be done???
Additional Questions:
1. What were your method(s) for extracting
accurate data in the face of difficulties you
encountered?
2. Using the data you obtained extrapolate the
length of string required for the period of
oscillation of the pendulum to equal 2 seconds.
Explain your process and show all work.
3. Assuming that the constant C equals 2π, find a
best-value for the acceleration due to gravity.
Explain your process and show all work.
Pendulum Laboratory Report
Grading Rubric:
1.Format:
2.Objectives and Procedures:
3.Analysis of results:
4.Error analysis:
5.Questions answered
10%
30%
30%
10%
20%
Sample Lab Report:
http://www.writing.engr.psu.edu/workbooks/labreport2.html
(Only difference is that you need to include data plots in the
body of your report, not just as an appendix.)
Pendulum Laboratory Report
3. Write-up
a) Typed, 12 pt font, 1.5 spacing
b) 3-5 pages long, not including appendix of data tables
c) Separate report into sections
d) Answer #1-3, making sure to cite all sources used
a) Describe the purpose of experiment
b) Describe the experiment and method
c) Describe the results
Include data plots and a description of what they
tell you – based off objectives
d) Describe possible errors that led your results to
be different from the theoretical values
Pendulum Laboratory Report
3. Write-up (continued)
e) How do your graphs and results support or refute
the theory of a simple pendulum? Your purpose
here is to discuss, in writing, what evidence there is
that indicates (or does not indicate) that the theory
is correct. Do not do any calculations for this
question. Instead, refer to the shapes, features,
and types of relations and equations shown on the
graph(s). Be sure to discuss each part of the lab.
Pendulum Laboratory Report
Grading Rubric:
1.Format:
2.Objectives and Procedures:
3.Analysis of results:
4.Error analysis:
5.Questions answered
10%
30%
30%
10%
20%
Sample Lab Report:
http://www.writing.engr.psu.edu/workbooks/labreport2.html
(Only difference is that you need to include data plots in the
body of your report, not just as an appendix.)