What Factors Affect the Period of Oscillation of a pendulum?

In this experiment we are trying to find if there is any relation be found between the weigh tied to the end of the string and the oscillation and also in a second experiment the relation to the length of string to the period of oscillation.

The first experiment

In the first experiment we are seeing if there is any relation between the weight tied to the end of the string and the period of oscillation. To conduct this experiment I shall be tying a piece of string to a stand and adding the appropriate weight to the string and releasing the string at approximately 45? and then timing for 10 oscillations and then recording the results on a table. The experiment will be done twice so to check for any error and to calculate a rough average then I shall divide it by 10 to find out the average time for 1 oscillation. The reason why I’m finding10 oscillations first is because it is hard to time 1 oscillation with an ordinary timer. Then I shall change the weights and repeat till I fill the table appropriately.

Equipment

In this experiment I will need…

One stand

One piece of string 20cm approximately

Various weights

Meter ruler

One timer

Protractor

One clamp

Prediction

My prediction is that the pendulum will swing at the same rate with no matter what the weight of the pendulum is this is based on a test that I found on Encarta encyclopaedia it had a two children on a swing one of and their was there different scenarios the third scenario it has a large boy on the first one and a small girl on the other with the same length of rope when u saw the two swinging you saw that they were swinging at the same rate. The caption said that Galileo concluded that the weight or the size of the pendulums ark does not affect the period of oscillation. The reason behind it is that because of the increase in weight has no effect on the gravity acting upon the bob it self. Once again it was Galileo who had proved this. It is believed that he demonstrated this by dropping two balls with different masses but with the same volume off of the Leaning Tower of Pisa and showed that two balls released at the same time at the top of the tower hit the ground at the same time as well.

Fair test

To make this a fair test the pendulum will be dropped at the same angle each time even though the angle should not make any affect to the results. Also the string length will not be changed through out the test.

Safety precautions

There are no obvious safety precautions to take in this experiment but care has to be taken when using the weights.

The reading I will be taking

The reading I will be taking is the weight attached to the string and the time it takes for 10 oscillations. I will be taking only one measurement and that is of the length of the string that will not be changed throughout the experiment, but because I am repeating the test I will be calculating the average from the two tests and finally from the averages I will be calculating how long it takes for one oscillation in seconds and recording that as well. The reason why I’m finding10 oscillations first is because it is hard to time 1 oscillation with an ordinary timer.

The test will be done twice for two reasons; one is to confirm that the experiment didn’t have any major errors and the second reason is that a rough average can be calculated from the two results.

With the results of this test I will be making a graph. This graph will be comparing the weight attached to the pendulum to the average time it has taken to do one oscillation.

The table I will be using for this experiment is shown below

Weight attached to the end of the string (g)

Test 1 of how long it takes for 10 oscillation in sec

Test 2 of how long it takes for 10 oscillation in sec.

Average time for 10 time oscillations in sec

Period of 1 oscillation in sec

100g

200g

300g

400g

500g

600g

The results should show according to my prediction that as the weight attached the period of oscillation should stay the same. So in theory all the results should be around the same time.

The complete range of results

Weight attached to the end of the string (g)

Test 1 of how long it takes for 10 oscillation in sec

Test 2 of how long it takes for 10 oscillation in sec.

Average time for 10 time oscillations in sec

Period of 1 oscillation in sec

100g

11.54

11.50

11.52

1.15

200g

11.54

11.60

11.57

1.16

300g

11.35

11.58

11.47

1.15

400g

11.49

11.53

11.51

1.15

500g

11.48

11.35

11.42

1.14

600g

11.28

11.34

11.31

1.13

Bellow is the graph I made showing the weight attached when compared to the average time taken for one oscillation

What the graph shows and what I can conclude from it.

Now as you can see the line of best fit is spoiled in this graph. This is because really this graph is looking too closely so the graph seem like there is no real correlation to the graph. When you look at the graph the range is only from 1.13 to 1.16 that is pretty small margin of error and also you have to consider that we were using a manual stopwatch so we have to account for human error.

I can conclude from this that the graph is looking too closely which only makes it look like there is no correlation to the bob and the time it takes for one oscillation. While really there is a strong relation

So when I look back at my prediction I can honestly say that my prediction was correct which was that the all the results would be similar and as the graph show the results are.

Evaluation of the experiment

On the whole the experiment was a success and it does show that the weight attached to the string has no effect on the period of oscillation. The method was fairly accurate but I would have preferred if I could have had a more accurate way of measuring the string and timing the pendulum. My prediction was correct thanks to the work of Galileo, which has proven to be quite helpful. Unfortunately the graph makes it look like the whole table is wrong but this is only because as previously stated was due to the fact that the graph was looking to closely at the results and if we were to do more tests and used a graph to larger scale you would see that there is a correlation in my results.

Improvement of the method

If I could I could redo the experiment and had more time and any equipment at my disposable I would have like to have an electronic timer of some sort that didn’t require a human to stop or start for 10 oscillations or even eradicate the need of doing 10 oscillations and jut do one. Also I would have like if we had used weights that were the same volume each time because in our experiment we were adding weights that increased in volume that decreased the length of string in the experiment. I think might have made some error to the result but probably not by much. Another thing I would like to do is to get more results with a more detailed range like for example rather than going up in 100 grams like I did this experiment I could go up in 50 grams instead.

THE SECOND EXPERIMENT

Method

In the second experiment we are looking at on how the length of string will affect the speed of oscillation. To conduct this experiment I will be tying a piece of string on top of a stand with help from a clamp at a certain length and at the bottom of the rope is a metal ball. The pendulum is released at a 45-degree angle and is timed for 10 oscillations then recorded and then the same test is repeated to check for errors and also from the two results an average can be taken. Once the experiment is done the string is extended and then the process starts again.

Equipment

The equipment we will need for this experiment will include…

1 bob

1 stand

1 clamp

1 Meter ruler

1 timer

1 80cm of string approximately

1 protractor

The same safety precautions will be maintained which was implied with the first, which was just to be careful with the weights.

Prediction

My perdition is that as the string is extended the period of oscillation. This is because of the longer string further the pendulum will have to travel further to make one oscillation. I believe this to be true because the as Galileo pointed out that the pendulum is not dependent on the weight attached or size of the pendulum’s ark, but on the length of the rod or string.

Fair Test

To make his a fair test I will be using the same bob through out the test and I will be releasing the pendulum at the same angle each time. Now I know that doing so is useless but also to make it a fair test I will be not changing the surrounding of where the pendulum experiment is done. Now this may seem a bit extreme but I might as well write it in because the place were the pendulum is does effect how the results come out. For example, this period will be greater on a mountain than at sea level.

Number of readings

Now all the reading will be the same as the first experiment in that I will be calculating how long it takes for 10 oscillations in sec for test 1 and test 2, the average time for 10 oscillations in sec and finally the period for 1 oscillation based on the average in seconds. The only difference is that in place the weigh attached in each experiment I will be showing in its place the length of the string in centimetres

This is the table I will be filling for the experiment.

Length of string (cm)

Test 1 of how long it takes for 10 oscillation in sec

Test 2 of how long it takes for 10 oscillation in sec.

Average time for 10 time oscillations in sec

Period of 1 oscillation in sec

In this table the experiment should show that the increases of the length of string should lead to the decreases in the period in oscillation.

Length of string (cm)

Test 1 of how long it takes for 10 oscillation in sec

Test 2 of how long it takes for 10 oscillation in sec.

Average time for 10 time oscillations in sec

Period of 1 oscillation in sec

19.8

9.93

9.91

9.92

0.99

30.3

11.81

11.55

11.68

1.17

40.2

13.19

13.37

13.26

1.33

50.2

14.73

14.53

14.63

1.46

59.8

16.04

15.94

15.99

1.60

70.01

17.00

17.35

17.16

1.72

As I predicted the period of oscillation increases the longer the string is this can be shown on a graph

Explanation of results and what I can conclude from it.

The experiment in general was very successful it because it shows that there is a relation to the length of string to the period of oscillation and that it shows that my theory was correct. The method that I use was fairly accurate but, the accuracy of the result is flawed because we have to account for that the stop watch was done manually and so we have to factor in human reaction time and that we couldn’t measure the string that well because we had to tie it from the top of the clamp which made it hard to measure when it was hanging freely from the clamp with a meter ruler.

Any unusual results

In this experiment there is not any really unusual results at all. None results that really sway off the line of best fit. The only reason I can give for the results that slightly sway off the line of best fit is because of human error.

What improvement would I have liked to make to the method if given the chance.

To get more reliable result I would like to have an electronic stopwatch that could stop and start automatically to reduce human error. Also I would have preferred if I could find a better way of increasing the string length and also a more accurate way of measuring the string because it was hard to make the string accurately. Also I would prefer if I could increase the string length in 5cm or less rather than in 10cm to get a more wider range of results also repeating the test a couple of more time would have helped as well because that way I could have made more accurate averages.

Bibliography

Original information that I previously know about pendulums I read from the book called Fatal Forces from the series called Horrible Science, which was written by Nick Arnold. The animation was found on Microsoft Encarta Standard edition 2002.