1. 2 December 2015
Final Project
PHYS-2010 & PHYS-2011
Cheyenne N Reed
MIDDLE TENNESSEE STATE UNIVERSITY

2. PHYS 2011-008 Cheyenne Reed
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L
IT JUST SWINGS THAT WAY
INTRODUCTION
Description:
This experiment is designed to study the movement of pendulums at different lengths while also
in a series. The lengths of each string will remain constant, the periods will be measured with a stop
watch,and our experiment will test whether the accepted formulas are proven by our measured results.
Purpose:
The purpose of this experiment is to understand pendulums and waves as a combined form of
motion. If a series of pendulums can create a wavelength or constant pattern when set up properly. The
questions we are hoping to answer with this experiment are: Does weight effect the pendulum’s motion?
Can a constant period be obtained? How many patterns could be made in a perfect system of pendulums?
Do the calculations match the measured values?
EXPERIMENT, MATERIALS, AND MEASURING DEVICES
Detail of Experiment:
We will use a wooden plank to pull the weights an even distance from their original
resting position and release them. We will count the number of wavelength changes that happen
before the weights come back to rest.
Equations that will be used during this experiment:
1
2
1
2
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
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L
g
T
T
f
f
L
g
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3. PHYS 2011-008 Cheyenne Reed
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Materials:
 Weights (8)
 Wooden Dowel
 Tape
 String
 Wooden Plank
The experiment uses eight even weights, eight uneven weights, tape, string, wooden dowel and a
wooden plank. The eight uneven weights were to test the effect of weight on the pendulum system, once
this was tested we moved to even weights. The string was tied to the weights and then taped to the
wooden dowel, the wooden plank was used to make sure the distance was equal for all weights lifted from
rest.
Uncertainties related to this experiment include time, length, degree and mass. These will be calculated
and accounted for in the final conclusion.
δ (m)= ?
δ (t) = .2 s
δ (l) = .005 m
δ (θ) = 2̊
Wave:
The Wave pictures represents the wavelengths we were able to capture from a video of the simple
pendulum machine, there are actually fourteen wave patterns that form with this machine; however, it
very difficult to capture all of them because they move through their series very quickly.

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DATA
Table 1.1- Period Measured and Calculated
Weight # Measured Period Calculated Period % Difference
1 .953 s .909 s 5 %
2 1.002 s .937 s 7 %
3 1.023 s .967 s 5%
4 1.053 s .9995 s 5%
5 1.099 s 1.04 s 5%
6 1.12 s 1.07 s 4%
7 1.17 s 1.11 s 5%
8 1.213 s 1.15 s 5%
Table 1.1 represents all of the times recorded and calculated for our experiment, the percent
difference shows the true difference between the two values. The difference in these values can be
associated with the model not being in a vacuum, human error and material malfunctions.
Table 1.2- Pendulum Measurements
Pendulum # 1 2 3 4 5 6 7 8
L .205 m .218 m .232 m .248 m .266 m .285 m .306 m .33 m
Table 1.2 shows the different lengths string used in our experiment with the weights.

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ANALYSIS
We followed a set of instructions to make a simple pendulum machine, this is what all of our
research has been over from YouTube videos and online science classrooms. For this model to work we
need exact lengths, any deviation from these lengths would cause the weights to move out of formation
due to their periods being altered.
MATHEMATICAL MODEL
Our mathematical models for this experiment are the following formulas:
1
2
1
2


















L
g
T
T
f
f
L
g


Calculations:

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Fractional Uncertainties:
Fu(L)= .005m/.261m= 0.019
Fu(t)=.2s/1.079s= 0.185
Fu(θ)= 2/10.75= 0.186
δ (m)= .0733 kg x 0.186= 0.0136 kg =0.01 kg
GENERAL CONCLUSION
We found that weight does not matter when working with a pendulum. Then length and
gravity have to remain the same for a pendulum to act in a constant period. There are 14 patterns
that are made with a simple pendulum machine, once it hits the 14
th
pattern it works its way
backwards through the pattern set. Our calculations were proven by our measured values, any
difference in the values can be attributed to the pendulums not being in a vacuum and human
error. This was a very fun experiment to preform and to watch how minute alterations can have
such a large impact on a system, as a whole. Air resistance is one of the forces that allows for the
system not have the same measured values as our calculated values, as well as minute problems
with the lengths of string.