Factors that affect the period of a pendulum
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Introduction
Physics Investigation: What factors affect the period of a pendulum?
By Tanya Waqanika
In this investigation, I will be looking at which factors affect the period (The time for one complete cycle, a left swing and a right swing) of a pendulum (a weight that dangles from a pivot so that it can swing freely). I will do this by tying a metal bob to a length of spring and dropping it from a certain height and measuring the time it takes to complete an oscillation, changing a variable for each of my preliminary investigations.
Independent Variable  Dependent Variable  Control Variables 
Length of String (continuous)  Period of the pendulum (continuous)  Diameter of Bob 
Type of Bob  
Angle bob dropped from  
Person stopping stopwatch  
Person dropping bob  
Height Bob is dropped from 
Preliminary Investigations
Preliminary One: Length of Strong
Results Table
Time of Period (seconds)  
Length of String  Trial 1  Trial 2  Trial 3  Ranges  Averages (mean) 
10cm  0.87  0.69  0.87  0.690.87  0.81 
20cm  1.01  1.02  1.01  1.011.02  1.01 
30cm  1.32  1.42  1.32  1.321.42  1.35 
40cm  1.66  1.71  1.66  1.661.71  1.68 
According to my graph, there is a positive correlation between the period of a pendulum and the length of string, meaning that as the length of the string increases, the period increases as well. The gradient of this graph is 0.9879. This would be ideal for my main investigation as there is a noticeable relationship between the length of string and period.
Preliminary Two: Angle Metal Bob is dropped from
Independent Variable  Dependent Variable  Control Variables 
Angle from which the bob is dropped from(continuous)  Period of the pendulum (continuous)  Diameter of Bob 
Type of Bob  
Same person dropping bob  
Same person stopping stopwatch  
Height bob is dropped from 
Results Table
Time of Period (seconds)  
Angle Bob is dropped from  Trial 1  Trial 2  Trial 3  Trial 4  Ranges  Averages (mean) 
90°  1.01  1.02  1.01    1.011.02  1.01 
80°  1.03  1.07  1.04  1.07  1.031.07  1.05 
70°  1.09  1.02  1.06  1.09  1.021.09  1.07 
60°  1.13  1.15  1.21  1.21  1.131.21  1.18 
A
This graph clearly shows a negative correlation between the period of a pendulum and the angle from which the bob was dropped. This shows that as the angle decreases, the time it takes to complete one full oscillation increases. The gradient of this graph is 0.8847. Although this can be considered for my main investigation, the gradient of this graph is shallower than the gradient of the first preliminary, meaning that my first preliminary is likely to give me more noticeable results than this preliminary.
Preliminary Three: Diameter of Bob
Independent Variable  Dependent Variable  Control Variables 
Diameter of Bob (continuous)  Period of the Pendulum (continuous)  Type of Bob 
Length of string  
Angle bob is dropped from  
Same person dropping bob  
Same person stopping stopwatch  
Height bob is dropped from 
Middle
Ranges
Averages (mean)
13mm
1.13
1.09
1.15
1.15
1.091.15
1.13
19mm
1.24
1.21
1.12
1.21
1.121.24
1.20
25mm
1.18
1.31
1.31

1.181.31
1.27
This graph also shows a positive correlation between variable and the period of the pendulum, meaning that as the diameter is increased, the time it takes the pendulum to complete one oscillation also increases. The gradient of the line of best fit on this graph is 1. This preliminary has yielded results that has a steeper gradient than my first preliminary, which means this is also ideal for my main investigation.
Preliminary Four: Type of Bob
Independent Variable  Dependent Variable  Control Variables 
Type of Bob (discontinuous)  Period of the pendulum (continuous)  Diameter of Bob 
Length of string  
Angle bob is dropped from  
Same person dropping bob  
Same person stopping the stopwatch  
Height Bob is dropped from 
Results Table
Time of Period (seconds)  
Type of Bob  Trial 1  Trial 2  Trial 3  Trial 4  Ranges  Averages (mean) 
Iron  1.01  1.02  1.01    1.011.02  1.01 
Brass  1.06  1.16  1.16    1.061.16  1.13 
Lead  1.10  1.21  1.14  1.21  1.101.21  1.17 
Copper  1.23  1.16  1.20  1.23  1.161.23  1.21 
According to this graph, there is a positive correlation between the type of bob used and period. The gradient of this graph is 0.9143. This gradient falls behind the ‘Length of String’ and ‘Diameter of Bob’ gradients, so it’s unlikely that I will use this for my main investigation, also, in terms of practicality, there wasn’t a large variety of materials to choose from.
Main Investigation: Length of String
I decided to choose Length of String for my investigation, because, my results for that preliminary had the one of most noticeable relationships between the independent and the dependent variable as well as the fact that there were no outliers.
I didn’t choose ‘Type of Bob, because ‘Type of Bob’ is an example of a discrete independent variable, in that it doesn’t have a numerical value that can be plotted on a graph. As well as this, even though there does appear to be a relationship between ‘Type of Bob’ and the period, there was another independent variable which was changed, which was the mass of each bob.
Although ‘Diameter of Bob’ was also ideal to be tested in my main investigation, it lost out to ‘Length of String’ simply because there was not a wide enough range of metal bobs that were made of the same material but had different diameter. So, although I predict it would’ve yielded noticeable results, Length of String is more practical to do, as well as the fact that the length of the string is easy to manipulate.

Conclusion
 Using a lighter sturdier form for the pendulum shaft instead of string, as the string had a tendency to bend throughout the oscillation, which could’ve affected the results
 Have a release that was positioned parallel to the clamp stand so that the angle from which the bob was dropped from each time was the same
 Having a way to hook the pendulum length/string to the clamp and the bob without having to tie knots so the length of the string that would swing was more accurate
Other than that, I believe my equipment was as accurate as I needed them to be, so I wouldn’t change any of the equipment I was using to carry out the experiment. I think that my results are reliable because the range bars are all relatively small on my graph, however in comparison to the Pendulum Equation; the results are too big and are in turn not scientifically accurate. I’ve calculated the average difference between my Averages and the Pendulum Equation line and have found it to be up to 0.4 of a second in difference. In conclusion, I believe that the length of string does affect the period of a pendulum, despite the inaccuracy of my results as my investigation proved that this factor still theoretically affects it.
This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.
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