Pendulum Lab
Question: What are the factors affecting the swing of the pendulum?
Hypothesis: The effects of
1. the weight
2. the height of the release
3. the length of the string
Experiment #1


Hypothesis: As weight increases, the time will stay the same.
Procedure: We will attach a string to a stand. At the end of the string, we will
attach a weight. We will then release the string and the weight, and we will
let it swing through the air. We will time how long it takes for the weight to
travel through the air and return to the starting point. After we record the
data, we will replace the original weight with one of a different mass. We will
repeat this process three times.
Trial
1
2
3
4
Mass (grams)
10
20
100
200
Time (seconds)
1.25
1.16
1.31
1.32
Experiment #2


Hypothesis: As the height of the release increases, so will the time.
Procedure: We will test the time a 100g weight attached to a string takes to
swing and return to its original position. We will then raise the height of
release and test the time, and then we will repeat two more times.
Trial
1
2
3
4
Height of release (centimeters)
20
30
40
50
Time (seconds)
1.16
1.16
1.12
1.22
Experiment #3


Hypothesis: We don’t think that the length of the string will affect the time.
Procedure: We will test how long it takes for a 100g weight attached to a
string to swing from one point and back to the same point. We will use
various lengths of string to test the times of the swing.
Trial
1
2
3
4
Length of String (centimeters)
17
30
37
60
Time (seconds)
.81
1.06
1.15
1.53
Conclusion
After completing three experiments, we concluded that the only factor affecting the time
of the swing of a pendulum was the length of the string (Experiment #3). The hypothesis
for Experiment #3 was incorrect, as was the hypothesis for the weight on the string
(Experiment #1). The time increased as the length of the string increased. The following
graph shows how the length of the string (the independent variable) affects the time (the
dependent variable). We choose a power model as the best fit to our data.
Time vs. Length
1.8
1.6
1.4
Time (s)
1.2
1
Time
Pow er (Time)
0.8
y = 0.1943x 0.4997
R2 = 0.9944
0.6
0.4
0.2
0
0
10
20
30
40
Length of String (cm )
50
60
70
Equation: Time = 0.1943(Length)0.4997
Explanation of equation: Time is the dependent variable measured in seconds. The
square root (approximately – 0.4997  0.5) of length, the independent variable, is
measured in centimeters. To make the present units (seconds equals the square root of
centimeters) work out and recognizing that gravity acts as part of the model, the equation
must include gravity [meters/(seconds)2] in the radicand and should be divided into
length for meters-centimeters to cancel and seconds squared to move to the numerator.
The constant of proportion between length and time in the equation is 0.1943, which is
similar to 2/980 (.2007), the value of a full cycle of the pendulum divided by gravity in
centimeters per second squared.
Therefore, the equation of the trend line is T = 2(L/g).5, the classic model.
Factors affecting data: human error in measurement of the string and the time of the
swing was measured by stopwatch.