Part 1: Period vs. Amplitude
MethodGoal, prediction, and method:
The goal of this lab is to investigate the period of a pendulum. From the model of the period
equation, the period of the pendulum does not change with respect to changes with the
amplitude. If the pendulum is swinging from different amplitudes, then the period of the
pendulum will remain the same. The experimental design is as follows: after assembling the
string into the ledge of the protractor, we can use the different angles to determine the period
for each amplitude. The stopwatch will be used to determine the time it takes for the
pendulum to swing back to its original position. We will use 4 different amplitudes to
determine and conduct the experiment with 8 trials. We will use 5 oscillations for each
measurement and record the time. Then we will take the average time it takes for one
oscillation.
Equipment:
● Stopwatch- to measure the time it takes for 5 oscillations
● Tape measurer- to measure the length of the string of the pendulum
● Protractor- to measure the different amplitudes of the pendulum
● Scissor- to cut the string of the pendulum
● 36.72 cm +/- 0.05cm string- used to hang the wight for the pendulum
● Silver weight- used as the weight in the pendulum
Statistical and Analysis Tools:
● Mean- in order to get the best estimate
● Standard Deviation- in order to get the uncertainty in single measurements
● Standard Deviation of the mean- in order to acquire the uncertainty in the mean value
● T-Score- shows if the data comparison is distinguishable or indistinguishable
○ t < 1 is indistinguishable
○ 1 < t < 3 is inconclusive
○ 3 < t is distinguishable
Variables:
The length of the string (36.72 cm +/- 0.05cm) and the weight used will be constant
throughout all the trials. The variable that we will be changing is the amplitude or the angle at
which the pendulum will be launched. The method used to record the time it takes will also
be constant as the group is going to use a stopwatch.
DataTable 1. Period times using stopwatch
Amplit
ude
Period
Trial 1
Period
Trial 2
Period
Trial 3
Period
Trial 4
Period
Trial 5
Period
Trial 6
Period
Trial 7
Period
Trial 8
10°
1.27s
+/0.01s
1.15s
+/0.01s
1.26s
+/0.01s
1.15s
+/0.01s
1.27s
+/0.01s
1.18s
+/0.01s
1.21s
+/0.01s
1.19s
+/0.01s
20°
1.19s
+/0.01s
1.21s
+/0.01s
1.21s
+/0.01s
1.22s
+/0.01s
1.22s
+/0.01s
1.23s
+/0.01s
1.19s
+/0.01s
1.20s
+/0.01s
40°
1.18s
+/0.01s
1.22s
+/0.01s
1.20s
+/0.01s
1.22s
+/0.01s
1.21s
+/0.01s
1.22s
+/0.01s
1.22s
+/0.01s
1.19s
+/0.01s
60°
1.24s
+/0.01s
1.24s
+/0.01s
1.25s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.25s
+/0.01s
1.25s
+/0.01s
1.23s
+/0.01s
Table 2. Statistical Analysis
Amplitude
Mean
Standard Deviation
Standard Deviation
of the Mean
10°
1.21s
0.051s
0.018s
20°
1.21s
0.015s
0.005s
40°
1.21s
0.015s
0.006s
60°
1.24s
0.009s
0.003s
Table. 3 T-Scores
Comparisons
T-Score
10° and 20°
0
10° and 40°
0
10° and 60°
1.639
20° and 40°
0
20° and 60°
4.851
40° and 60°
4.851
ConclusionThe data does somewhat support that the period is independent of the amplitude since half of
the t-scores calculated showed that the data was indistinguishable. In addition, the mean for
the amplitudes of 10°, 20°, 40° were all 1.21s, indicating how similar the period was for the
different amplitudes. The uncertainty of the experiment was the precision of the stopwatch, as
it only goes to the hundredths place. An improvement to this experiment could be using a
more accurate way to record the period of the pendulum, eliminating human error. Compared
with the prediction, the data supported the idea that the period was independent of the
amplite, proving the hypothesis correct.
Part 2: Period vs Amplitude Redux
MethodGoal, prediction, and method:
The goal of the second part of this lab is to improve the confidence in the measurements so
that the overall confidence is increased in the conclusions. If the pendulum is swinging from
different amplitudes, then the period of the pendulum will remain the same. The experimental
design is as follows: after assembling the string into the ledge of the protractor, we can use
the different angles to determine the period for each amplitude. We will be using a PASCO
photogate program to record the time for each period. We will use 4 different amplitudes to
determine and conduct the experiment with 8 trials. We will use 5 oscillations for each
measurement and record the time. Then we will take the average time it takes for one
oscillation. Using the PASCO photogate instead of the stopwatch will eliminate random
uncertainty because it reduces the varying reaction times associated with the stopwatch.
Equipment:
● PASCO photogate- to measure the time it takes for 5 oscillations more precisely
● Tape measurer- to measure the length of the string of the pendulum
● Protractor- to measure the different amplitudes of the pendulum
● Scissor- to cut the string for the pendulum
● 36.72 cm +/- 0.05cm string- used to hang the wight for the pendulum
● Silver weight- used as the weight in the pendulum
Statistical and Analysis Tools:
● Mean- in order to get the best estimate
● Standard Deviation- in order to get the uncertainty in single measurements
● Standard Deviation of the mean- in order to acquire the uncertainty in the mean value
● T-Score- shows if the data comparison is distinguishable or indistinguishable
○ t < 1 is indistinguishable
○ 1 < t < 3 is inconclusive
○ 3 < t is distinguishable
Variables:
The length of the string (36.72 cm +/- 0.05cm) and the weight used will be constant
throughout all the trials. The variable that we will be changing is the amplitude or the angle at
which the pendulum will be launched. The method used to record the time it takes will also
be constant as the group is going to use the PASCO photogate this time.
DataTable 4. Period times using PASCO photogate
Amplit
ude
Period
Trial 1
Period
Trial 2
Period
Trial 3
Period
Trial 4
Period
Trial 5
Period
Trial 6
Period
Trial 7
Period
Trial 8
10°
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
1.23s
+/0.01s
20°
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
1.24s
+/0.01s
40°
1.26s
+/0.01s
1.26s
+/0.01s
1.26s
+/0.01s
1.26s
+/0.01s
1.26s
+/0.01s
1.26s
+/0.01s
1.26s
+/0.01s
1.16s
+/0.01s
60°
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
1.31s
+/0.01s
Table 5. Statistical Analysis
Amplitude
Mean
Standard Deviation
Standard Deviation
of the Mean
10°
1.23s
0s
0s
20°
1.24s
0s
0s
40°
1.26s
0s
0s
60°
1.31s
0s
0s
Table 6. T-Scores
Comparisons
T-Score
10° and 20°
indistinguishable
10° and 40°
indistinguishable
10° and 60°
indistinguishable
20° and 40°
indistinguishable
20° and 60°
indistinguishable
40° and 60°
indistinguishable
ConclusionThe new method revealed that as the magnitude of the angle increased, so did the period time
by very little. However, this time increase is very little and could have been caused by human
error of pushing the pendulum or accidentally changing the location of the photogate device.
Based on the T-score data, the period is not dependent on the amplitude because based on the
preciseness of our data, the comparisons of the different amplitudes are indistinguishable. It
did agree on what we found in part one because it was mostly the same result then also. Part 2
was more precise because the standard deviation was 0, resulting in a statistical uncertainty to
be 0 also. We are confident in our conclusion because based on using 2 different methods for
collecting the time for a period, we found that amplitude does not significantly affect the
period of the pendulum. One limitation to this lab was that if the standard deviation of two
data sets were both zero then the formula for the t-score would not work. As a result, you had
to infer that the data sets were indistinguishable because they were so very precise. Our
prediction still supports our data. One change that could be made to the lab is to use a device
not so precise that the standard deviation equals zero, and the t-score formula becomes
inapplicable. They could use the Phyphox app, where the phone itself would be the
pendulum, reducing random uncertainty.