How a Pendulum Works
An Investigation into How a Pendulum Works
Isaac Olson
Mitch Koebnick, Kyle Orr
13 September 2013
A Period
Purpose
There are three purposes of this experiment. The first purpose is to determine the relationship of the period and the amplitude of the pendulum. The second purpose is to determine the relationship of the period and the mass of the pendulum. The final, but most certainly not the least, purpose of this experiment is to determine the relationship of the period and the length of the pendulum.
Procedure
The procedure to this experiment is quite simple. First, hang a piece of string from some sort of high balcony, or in this case the ceiling. Next, take a mass and hook (or tie) it to the end of the string. Then use a clinometer to measure the string at various angles before swinging the pendulum. Next, use a stopwatch to measure the time it takes for the pendulum to swing back and forth ten times and then divide the time by ten to get the average time it takes a pendulum to swing back and forth one time. This procedure was repeated for different changes in mass, amplitude, and length.
Results
The raw experimental data is tabulated below:
A
(deg)
5
10
15
20
25
T
(s)
2.46
2.5
2.5
2.5
2.53
Length and mass are constant
M
(kg)
1
1.2
1.4
1.9
2
T
(s)
2.54
2.54
2.54
2.53
2.5
Amplitude and length are constant L
(m)
0.41
0.84
1.53
1.83
1.95
T
(s)
1.25
1.84
2.5
2.65
2.79
Amplitude and mass are constant
There is a linear relationship between the square of the period of a pendulum and its length. The strong correlation of 0.9982 is also evidence of the linear behavior of the data. As the length increases, so does the period. The equation of the graph is T2 = 3.956L +0.01117. However, since 0.01117 is less than 0.5% of the range, we can ignore the range, making our equation T2 = 3.956L.The graph compares favorably to the theoretical equation T2=4L.
Conclusion
Isaac Olson
Mitch Koebnick, Kyle Orr
13 September 2013
A Period
Purpose
There are three purposes of this experiment. The first purpose is to determine the relationship of the period and the amplitude of the pendulum. The second purpose is to determine the relationship of the period and the mass of the pendulum. The final, but most certainly not the least, purpose of this experiment is to determine the relationship of the period and the length of the pendulum.
Procedure
The procedure to this experiment is quite simple. First, hang a piece of string from some sort of high balcony, or in this case the ceiling. Next, take a mass and hook (or tie) it to the end of the string. Then use a clinometer to measure the string at various angles before swinging the pendulum. Next, use a stopwatch to measure the time it takes for the pendulum to swing back and forth ten times and then divide the time by ten to get the average time it takes a pendulum to swing back and forth one time. This procedure was repeated for different changes in mass, amplitude, and length.
Results
The raw experimental data is tabulated below:
A
(deg)
5
10
15
20
25
T
(s)
2.46
2.5
2.5
2.5
2.53
Length and mass are constant
M
(kg)
1
1.2
1.4
1.9
2
T
(s)
2.54
2.54
2.54
2.53
2.5
Amplitude and length are constant L
(m)
0.41
0.84
1.53
1.83
1.95
T
(s)
1.25
1.84
2.5
2.65
2.79
Amplitude and mass are constant
There is a linear relationship between the square of the period of a pendulum and its length. The strong correlation of 0.9982 is also evidence of the linear behavior of the data. As the length increases, so does the period. The equation of the graph is T2 = 3.956L +0.01117. However, since 0.01117 is less than 0.5% of the range, we can ignore the range, making our equation T2 = 3.956L.The graph compares favorably to the theoretical equation T2=4L.
Conclusion