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Simple Harmonic Motion Physics HL Lab Report

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Introduction

Planning (a)

In this experiment, I will attempt to investigate the dependence of the period (T) of a simple pendulum on the length (L) of the string used. The motion of a pendulum can be considered simple harmonic motion even though the bob hanging at the end of the string moves in curves. This is because if the string is relatively long compared to the initial displacement, the curve made by the bob is close enough to a straight line. I expect that the period (T) will be directly proportional to the length (L) of the string. I will make sure that I start the pendulum swing from the same amplitude. This means it will always start with the same gravitational potential energy as it starts swinging from the same point, and hence its maximum speed will remain the same for all lengths of the string. I expect that as the length (L) is reduced, the period (T) will decrease as the pendulum will have to cover less distance during each complete swing.

During this experiment, the length (T) of the string will be the independent variable, altered throughout the experiment. The dependent variable in this experiment will be the period (T) of the simple pendulum. The controlled variables throughout the experiment will be the mass (M)

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Middle

Due to the reaction time in starting and stopping a timer, the uncertainty in the total time X will be about ± 0.5 s

Length

L/cm

± ΔL = ± 0.3cm

Reading 1

X/s

± ΔX = ± 0.5 s

Reading 2

X/s

± ΔX = ± 0.5 s

Reading 3

X/s

± ΔX = ± 0.5 s

50 cm

30 s

29 s

30 s

40 cm

25 s

26 s

26 s

30 cm

23 s

22 s

22 s

20 cm

19 s

19.5 s

20 s

10 cm

15 s

14 s

14 s

Data Processing and Presentation

As I had predicted that the period (T) will be directly proportional to the length (L) of the string, this will be verified by plotting a graph of length (L) versus period (T)

First we have to calculate the average out of the 3 readings after which we can calculate the period (T) of the pendulum by dividing the average recorded values by 10 as 10 swings were taken for each reading and I shall round them off to 2 significant figures

Length

L/cm

± ΔL = ± 0.3cm

Reading 1

X/s

± ΔX = ± 0.5 s

Reading 2

X/s

± ΔX = ± 0.5 s

Reading 3

X/s

± ΔX = ± 0.5 s

Average Reading

R/s

± ΔR = ± 0.5 s

50 cm

30 s

29 s

30 s

29.7

40 cm

25 s

26 s

26 s

25.7

30 cm

23 s

22 s

22 s

22

20 cm

19 s

19.5 s

20 s

19.5

10 cm

15 s

14 s

14 s

14

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Conclusion

There may also have been errors caused due to human reaction time in stopping the watch while determining the exact moment when the pendulum reached the highest point of its trajectory.

Improvements that can be made for the adopted procedure:

  • A clamp can be used to hold the bob at the required angle before setting it in motion to avoid any initial push it may have received. Also, this will solve the problem of a slightly circular path being followed due to unsteady hands as the clamp will be perfectly steady during all trials.
  • String of a longer length can be used as this will  increase the accuracy in the following 2 ways:
  • Any error due to the instruments used in the measurement of the length will not be as noticeable with a longer length as compared to a shorter one.  In other words, an error of 0.3 cm is more significant with string length of 20cm than it is with a string length of 100cm.
  • Due to a longer string length, the period will also be longer and hence any errors due to the human reaction time in the measurement of the period will be substantially reduced.
  • The flight path of the pendulum can also be made straighter by restricting it by placing 2 glass screens on both sides. The closer they are kept, the more straight the path it will follow. However, care should be taken to ensure that the string does not come into contact with the glass screens as this will affect its path.

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