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To investigate the factors, which affect the swing of a pendulum.

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Introduction

Pendulum Experiment

Aim: To investigate the factors, which affect the swing of a pendulum.

Preliminary: In order to find out which factors would be best to investigate I decided to carry out some preliminary work. Before I started this however I needed to find the best way of timing my experiment. To do this I tried a number of different ways whilst keeping the angle, length of string and mass of my simple pendulum the same.

Results:

Way

Time (sec)

Average time per swing (sec)

10 swings- from end

25.41

2.51

10 swings- from middle

25.81

2.58

5 swings- from middle

12.65

2.53

1 swing- 3 times- from middle

2.63, 2.47, 2.31

2.47

From my results I decided that the most accurate way of timing was by doing 5 swings from the mid point of the pendulum. This is because it was much easier to know when to start and stop the stopwatch as you could see clearly when the bob was at the same point, which was much harder if you tried to time from the point where the bob was released. I chose 5 swings as I felt it would be less likely for the pendulum to start to slow down.

Next I decided to carry out another few preliminary experiments to aid me in deciding which factors to further investigate in my main experiment. To allow me to see if the factor I was testing had any affect on the swing of my pendulum I changed only one thing at a time. My results were as follows:

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Middle

100

30

6.28

6.28

6.28

75

100

30

7.71

7.72

7.715

100

100

30

8.65

8.67

8.66

Changing the Length of the string:

Here my results show a clear pattern. As the length of string was increased the time it took the pendulum to oscillate is also increased. I am therefore going to investigate this further. In order to be able to make a clear conclusion I have decided that it would be best to collect about 10 results.

Hypothesis: I predict that as the length of the string is increased so will the time it takes the pendulum to oscillate. I have seen this in my preliminary experiment but also as I know that the start position and mass don’t affect the swing of a pendulum the length of string therefore must. This is because as it is increased the bob has further to travel in order to complete a swing. As the angle has not changed, neither has the potential energy. Also the force remains the same, as the mass has not changed. So the bob has further to go with the same energy and acceleration. Hence it will move slower and take longer to oscillate.

I also predict that the relationship between these two factors is in some way proportional. This is because I know from background information I found in a textbook the equation for the period of a simple pendulum is:

T=2∏ √L

           g

This can then be rearranged to give the formula:

T²=4∏²L

g

I know that:

Gradient= y

x

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Conclusion

I can see how accurate my results are by using the equation T²=4∏²L  and swapping in my results.                                                      g

The gradient for my graph of time² against length is

1.0 (sec)  = 3.33’

0.3 (m)

If my results were completely accurate the gradient should actually have been:

4∏²  =  4∏²  = 3.95(2dp)

  g         10

Also I can check my results against gravity, which should equal 10.

1²= 4∏² 0.3     g= 4∏²x0.3      g=11.84(2dp)

        g                      √1

So my result were not totally accurate, although they were not too far out and the degree of accuracy can mostly be accounted for.

Evaluation: Although my results were not entirely accurate they still follow roughly the right pattern. The most likely reason for any mistake is probably an error in timing. This is because it was hard to start and stop timing at exactly the right point and also some leeway must be given for human reaction rate. Another reason for inaccuracy might be that the way the string was attached to the clamp stand, which meant that there was sometimes some friction caused. If I were to carry out the experiment again I would have two people timing so that averages could be taken. Also I would mark the centre point with some brightly coloured card so it was easier to see. I might also take the average of 10 swings rather than five, so that when timing you would have more time to react but also that any timing error would be less significant to the results.

Jemma Millhouse

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