Betlejewski 1
Hailey Betlejewski
Partners: Elizabeth B., Jean S., Nicki K.
9 October 2013
PHYS 1051L, Sec 35
The Effect the Spring Constant, Stretch Distances and Mass Have on the Period of Oscillation
Abstract
The question investigated in this experiment was, what affects the period of oscillation of a
spring/mass system? Based on this question, our hypothesis is that the period of oscillation is
impacted only by the mass. In order to address this question, an experiment was done testing to
see if the spring constant, the mass used and the stretch distance impacted the period of
oscillation. The spring constant was found by using 5 different springs with the same mass and
finding the slope of each. Each variable was tested separately to see if they solely impacted the
period. Each test used the same system to measure the period and each had the same dependent
variable. The dependent variable was always the period of oscillation. The independent variable
varied based on what was tested; either the mass, stretch distance or spring type. Each had their
own control variables to that fit with its specific experiment. Data from our experiment was
compared to two other groups. The results showed that the mass used and the spring constants
were the variables that had an impact on the period of oscillation. As the mass increases, the
period of oscillation increases. Also as the spring constant decreases, the period of oscillation
increases. This is supported with the data from the two other groups as well as our own results.
Based on our results, our hypothesis is supported but needs to be revised because it is not the
only variable impacting the period. The new hypothesis would be the period of oscillation is
impacted by the spring constant and the mass.
Experimental Design
Effect of Mass
Hypothesis:
Independent Variable:
Dependent Variable:
Control Variables:
Effect of Stretch Distance
Hypothesis:
Independent Variable:
Dependent Variable:
Control Variables:
The period of oscillation is impacted by the
mass used.
Mass used.
Period of oscillation.
Spring/mass system used, spring used (C1),
stretch distance (40cm)
The period of oscillation is impacted by stretch
distance used.
Stretch distance.
Period of oscillation.
Spring/mass system used, spring used (C1),
mass used (250g)
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Effect of Spring Constant
Hypothesis:
The period of oscillation is impacted the spring
used
Spring used.
Period of oscillation.
Spring/mass system used, stretch distance
(5cm), mass used (250g)
Independent Variable:
Dependent Variable:
Control Variables:
Results
Table 1. This group of tables represents the data collected from our group. They are set up this
way in a group to show side by side which variables impacted the period of oscillation and which
ones didn’t. Each variable was tested: mass, spring constant, and stretch distance. Stretch
distance had no impact on the period but the other two variables did. As the mass increases, the
period increases. As the spring constant increases, the period decreases. The stretch distance
stayed constant. The uncertainties for each period are also shown.
(a)
Mass(g)
150
200
250
300
350
(b)
Spring
Constant
(cm)
19.4 ± .77
33.7 ± .20
51.6 ± .23
55.8 ± .55
77.7 ± .25
Period of
Oscillation
.634 ± .0017
.748 ± .0068
.810 ± .0037
.890 ± .0033
.949 ± .0094
Period of
Oscillation
.812 ± .0049
.548 ± .0025
.431 ± 7.6e-4
.425 ± 4.6e-4
.352 ± 9.5e-4
(c)
Stretch
Distance
(cm)
5
10
15
20
25
Mass vs. Period
1.2
Period (seconds)
1
y = 0.061x0.4694
R² = 0.9943
0.8
0.6
Series1
0.4
Power (Series1)
0.2
0
0
100
200
Mass (grams)
300
400
Period of
Oscillation
.812 ± .0049
.817 ± .0014
.815 ± .0016
.859 ± .0042
.874 ± .016
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Figure 1. This graph shows the mass vs. the period of oscillation. As you can see, as the mass
increases, the period of oscillation also increases at a constant rate. This data is strictly from our
group and reflects the results in Table 1(a).
Period (secojnds)
Spring Constant Vs. Period
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
y = 4.6766x-0.599
R² = 0.9926
Series1
Power (Series1)
0
20
40
60
80
100
Spring Constant (N/m)
Figure 2. This graph shows the spring constant vs. the period of oscillation. As you can see, the
period decreases as the spring constant increases. This data is strictly from our group and reflects
the results in Table 1(b).
Period (secojnds)
Stretch Distance vs. Period
0.9
0.89
0.88
0.87
0.86
0.85
0.84
0.83
0.82
0.81
0.8
0.79
y = 0.7459x0.0439
R² = 0.6597
Series1
Power (Series1)
0
10
20
30
Stretch Distance (cm)
Figure 3. This graph shows the stretch distance vs. the period of oscillation. As you can see,
there really is no pattern being shown. While there are two higher periods, this can be from error.
This data is strictly from our group and reflects the results in Table 1(c).
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Table 2. This group of tables represents the data collected from Group 5. They are set up this
way in a group to show side by side which variables impacted the period of oscillation and which
ones didn’t. Each variable was tested: mass, spring constant, and stretch distance. Stretch
distance had no impact on the period but the other two variables did. As the mass increases, the
period increases. As the spring constant increases, the period decreases. The stretch distance
stayed constant. The uncertainties for each period are also shown.
(a)
(b)
(c)
Mass(g)
Period of
Spring
Period of
Stretch
Period of
Oscillation
Constant
Oscillation
Distance
Oscillation
(cm)
(cm)
100
.380 ± .0034
4
.347 ± .0042
5.3 ± .0096
1.10 ± .004
150
.479 ± .0076
5
.351 ± .0041
7.8 ± .013
.985 ± .0098
200
.509 ± .0054
6
.354 ± .0011
33.7 ± .35
.453 ± .003
250
.551 ± .0053
7
.348 ± .0006
49.4 ± .62
.38 ± .0022
300
.607 ± .0072
85.6 ± 1.4
.146 ± .0082
8
.348 ± .0024
Table 3. This group of tables represents the data collected from Group 6. They are set up this
way in a group to show side by side which variables impacted the period of oscillation and which
ones didn’t. Each variable was tested: mass, spring constant, and stretch distance. Stretch
distance had no impact on the period but the other two variables did. As the mass increases, the
period increases. As the spring constant increases, the period decreases. The stretch distance
stayed constant. The uncertainties for each period are also shown.
(a)
Mass(g)
150
200
250
300
350
(b)
Period of
Oscillation
.285 ± 1.4e-4
.329 ± 1.6e-4
.365 ± 1.6e-4
.399 ± 1.2e-4
.430 ± 2.3e-4
Spring
Constant
(cm)
7.78
29.3
50.7
55.3
70.4
(c)
Period of
Oscillation
1.12 ± 5.5e-4
.54 ± 2.6e-4
.46 ± 9.3e-3
.43 ± 2.6e-4
.36 ± 1.1e-4
Stretch
Distance
(cm)
2
4
5
6
7
Period of
Oscillation
.37 ± 1.8e-4
.37 ± 7.3e-4
.37 ± .0051
.37 ± .0011
.37 ± .0011
Conclusion and Discussion
Our hypothesis states that the period of oscillation is impacted by the mass used. After
completing this experiment, we can support our hypothesis. However, our hypothesis can be
supported but it must be revised because the mass wasn’t the only variable that impacted the
period of oscillation. The new hypothesis would be the period of oscillation is impacted by the
mass used and the spring constant. We were to find what impacts the period of oscillation of a
spring/mass system. The variables that had an impact on the period of oscillation were the mass
used and the spring constant. We have found based on our own groups’ results that as the mass
increases, the period also increases. This is shown clearly in Table 1(a).You can see in this table
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that the period is increasing as the mass increases. This is also supported by the Group 5 and
Group 6 data shown in Table 2(a) and Table 3(a)—they show the same patterns as our data.
Visually you can see the linear pattern in Figure 1. Not only did we discover this but we can
conclude that as the spring constant increases, the period of oscillation decreases. This evidence
is clearly shown in Table 1(b). You can see clearly that when the spring constant increases, the
period of oscillation decreases. This is also supported by Group 5 and 6. They show the same
results which can be seen in Table 2(b) and Table 3(b). Table 1(c) also shows that the stretch
distance does not impact the period of oscillation because the periods stay constant as the stretch
distance differs. Group 5’s data (Table 2(c)) and Group 6’s data (Table 3(c)) supports this claim
because they too have a constant period when different stretch distances were used. This is
visually shown in Figure 3. There is no pattern that shows in the graph and the first three points
are rather constant. These results show that the mass impacts the period of oscillation. This
makes logical sense that the period would increase as the mass increases because the more
weight there is, the more stretched out the spring will become causing a larger period. It also
makes logical sense that the spring constant would impact the period of oscillation. It makes
logical sense because each spring constant represents a different type of spring. Each spring
stretches in its own way—some stretch more than others and so on. If they are different springs
they are bound to stretch differently causing a difference in the period of oscillation. It also
makes logical sense that the stretch distance would have no impact on the period of oscillation.
This is because it shows where the equilibrium is but would not impact the period.
The experiment was run electronically through data studio which leaves little room for human
error since all the data was recorded on a computer. Human error could be incorrect
measurements of the masses used or incorrect measurements of the spring constants. There are
some data that falls outside of the identified pattern in our data in Table 1(c). The last two
periods seem higher than the rest and don’t really fit. Random errors like this can be caused by
incorrectly measuring the periods on the computers part. Not every measurement can be perfect,
not even if it is done electronically. These random errors can be decreased by running more trials
in order to minimize error by averaging over a larger number of periods obtained. Without the
presence of random error incorrectly measuring the period of oscillation for the last two
measurements in the stretch distance vs. time would be closer to the first three measurements. A
systemic error that could have happened would be the added weight of the paper card on the
spring/mass system that was used. The paper was never weighed and that could have influenced
results by having a heavier mass than intended. This could easily be avoided by taking if off and
weighing it. A constraint I noticed in this experiment was that some of the springs were hard to
stretch making it hard to measure at the same stretch distance. Aside from any errors that may
occur, the results showed that as the mass used on the system increases, the period of oscillation
also increases. It also showed that as the spring constant increases, the period of oscillation
decreases. Based on our own results and the results of Group 5 and 6 our original hypothesis is
supported but can be revised because the mass wasn’t the only variable to impact the period of
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oscillation. The new revised hypothesis would be, the period of oscillation is impacted by the
spring constant and the mass used.
References
The data referenced in this experiment was shared in class during lab 8. It is the results from
Group 5 and Group 6.