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Investigate the factors affecting the time period of a pendulum

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Introduction

Pendulum Coursework

Aim:

To investigate the factors affecting the time period of a pendulum

Introduction:

The time period of a pendulum is the amount of time that a pendulum takes to swing from position A, through positions B and C and back to A again. It is the movement from 1 peak to another, i.e. one oscillation.  I need to examine the factors affecting how long it takes for 1 oscillation to take place, In relation to the energy transfers involved. After I have done this I can decide which factor to use as a variable and which factors that I should keep the same.image00.png

Factors affecting the time period of a pendulum

Length of String:

The Length of the string will affect the time period of a pendulum because it will mean that the pendulum travels a greater distance in its oscillation.  The path of the pendulum is like an arc on the bottom of circle, with the piece of string as a radius. Thus, according to the circle theorem: C=2πr, the circumference of the circle will increase, and so will the length of length of the arc. This increases the distance travelled by the pendulum, and therefore the time taken.

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Middle

0.3

1.098910442

0.4

1.268912479

0.5

1.41868728

0.6

1.554094051

0.7

1.678613427

0.8

1.794513237

0.9

1.903368718

1

2.006326792

If I plot these points onto a graph, I would expect it to be a straight line as T is proportional to l, as l is the only factor in my experiment that is variable.

image06.png

As you can see, this line is not straight, I must now refer back to my formula to obtain a straight line. If we ignore all of the constants, we can see that T is proportional to   l, and therefore a graph portraying T2/l should give us a straight line:

This is a straight line, which proves that Tsq. Is proportional to l.image07.png

Method:

  1. Set up equipment as shown in diagram
  2. Pull the string through the pieces of wood until there are 10 cm of string between the wood and the pendulum
  3. Pull the pendulum out so that the string is at 10°.
  4. Let the pendulum go and let it swing
  5. Once the pendulum gets to the top of its swing, in either position A, or position C, start the stopwatch.
  6. Count each time the pendulum returns to that position.
  7. Once you get to 10, stop the stopwatch
  8. Repeat steps 3-7 3 times.
  9. Keep changing the length of the string in 10 cm steps and repeat steps 3-8 until you get to 1 meter.

Fair test:

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Conclusion

2" colspan="1" rowspan="1">

0.8

18.22

18.5

18.31

18.34333

0.9

19.22

19.32

19.35

19.29667

1

20.35

20.22

20.31

20.29333

Using the above table I will produce a table of the average time period.

length (m)

Average time period

0.1

0.722333333

0.2

0.962333333

0.3

1.157666667

0.4

1.304333333

0.5

1.442666667

0.6

1.582333333

0.7

1.702

0.8

1.834333333

0.9

1.929666667

1

2.029333333

I will now calculate the percentage error from my predicted results to my actual results.  

length (m)

Average time period

Percentage Error

0.1

0.722333333

13.85077

0.2

0.962333333

7.252854

0.3

1.157666667

5.346771

0.4

1.304333333

2.791434

0.5

1.442666667

1.690252

0.6

1.582333333

1.81709

0.7

1.702

1.393208

0.8

1.834333333

2.218992

0.9

1.929666667

1.381653

1

2.029333333

1.1467

I can check the accuracy of my experiment again by plotting a graph of Tsq. against length and calculate the gradient.

image08.png

The gradient = change in y / change in x

The gradient = 4

Tsq./l=4

If I rearrange the formula, I can see that:

Tsq/l=4πsq./g

4πsq./4=g

4πsq./4=9.87.  This is an error margin of 0.6%, this shows that my experiment was quite accurate

Conclusion:

From this experiment I was able to prove that Tsq. Is proportional to l: i.e. when Tsq. Doubles, so does l. From this I can conclude that l, is the key factor which directly affects T.

Evaluation:

The experiment was quite accurate as it produced an error margin of only 0.6%.   However, comparing predicted results to my results I found a 13% error margin in some cases.  This was when the pendulum was at its shortest length and therefore had its shortest difference to travel, which meant that the time periods were very quick, and therefore harder to calculate.  This may have led to my inaccuracies.

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