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# 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 0.69-0.87 0.81 20cm 1.01 1.02 1.01 1.01-1.02 1.01 30cm 1.32 1.42 1.32 1.32-1.42 1.35 40cm 1.66 1.71 1.66 1.66-1.71 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 - 1.01-1.02 1.01 80° 1.03 1.07 1.04 1.07 1.03-1.07 1.05 70° 1.09 1.02 1.06 1.09 1.02-1.09 1.07 60° 1.13 1.15 1.21 1.21 1.13-1.21 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

Trial 4

Ranges

Averages (mean)

13mm

1.13

1.09

1.15

1.15

1.09-1.15

1.13

19mm

1.24

1.21

1.12

1.21

1.12-1.24

1.20

25mm

1.18

1.31

1.31

-

1.18-1.31

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 - 1.01-1.02 1.01 Brass 1.06 1.16 1.16 - 1.06-1.16 1.13 Lead 1.10 1.21 1.14 1.21 1.10-1.21 1.17 Copper 1.23 1.16 1.20 1.23 1.16-1.23 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.

 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

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.

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