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• Level: GCSE
• Subject: Maths
• Word count: 1829

# Investigation of a simple pendulum and what effects it the time period?

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Introduction

Investigation of a simple pendulum and what effects it the time period?

## Simple pendulum

A simple pendulum consists of a mass suspended on a length of string, which is allowed to ‘freely’ swing. To complete one oscillation the mass must swing from one side to the other and back again. The time of each oscillation will be recorded.

Diagram

There are several possible variables, which could affect the results of the time period.

• Weight of the mass
• Length of string
• Point of displacement
• Differing the shape of the mass
• Thickness of string

## Chosen variable

I have chosen to vary the length of the string as the variable. This is because it appears in the formula for the time period of one oscillation therefore it must affect the time period. Also there are no practical problems as there would be with varying the shape of the mass. This would be almost impossible to come to any clear conclusion as the way different shapes affect the time period, as there would be no clear mathematical formula that could be used. There is an infinite number of ways in which a shape can be changed, and coming to a clear conclusion about the way in which the time period would be impossible.

Furthermore, varying the length of string and timing the oscillations only requires simple equipment (a ruler and a stop watch)

Middle

20

9.25

9.60

9.68

0.95

25

10.59

10.78

10.59

1.07

30

11.85

11.71

11.66

1.17

35

12.40

12.16

12.06

1.22

40

12.79

13.18

12.99

1.28

45

13.74

13.94

13.71

1.38

50

14.21

14.43

14.48

1.44

55

15.19

15.15

15.13

1.52

60

15.71

15.60

15.85

1.57

65

16.28

16.30

16.38

1.63

70

16.82

16.46

16.73

1.69

75

17.43

17.47

17.57

1.75

80

18.32

18.60

18.41

1.82

85

18.91

19.15

18.86

1.90

90

19.17

19.22

19.34

1.92

95

19.51

19.83

19.72

1.97

100

22.10

21.60

22.60

2.21

These results are all measured to 2 decimal places. The average column is rounded to 2 decimal places as you cannot improve accuracy by finding the mean.

A table to show the difference between the formula results and the experimental

 Seconds (2dp) Seconds (2dp) Seconds(2dp)

Conclusion

My results were accurate as I had already improved on my method from the preliminary results and had found it was more accurate to work in a team with one person timing and the other releasing the mass.

There are ways of improving this experiment. The one I believe would make most difference is eradicating human error and placing this responsibility upon machines as the human reaction time is poor and is only reliable to one decimal place. Also to take more results at closer intervals over a wider range of length would be sensible to see how the times progressed. Also conditions for the experiment to take place could be improved in a more controlled environment not a crowded school classroom.

There were three irregular results for one particular length: a 100cm. These showed not to correlate with the formula and were out of place on my graph. This is a good sign that irregularities are clear, as my results are very accurate. This is the only result that needs extra attention and to extend the experiment I would repeat this particular length.

To extend the experiment I could change any of the other variables suggested in my plan. Such as weight or shape of mass. These would create a wider more advanced knowledge of how a simple pendulum works.

This student written piece of work is one of many that can be found in our GCSE Comparing length of words in newspapers section.

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