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GCSE Twenty-first century science: Data collection and Analysis Investigation: The Oscillation of a simple pendulum

Rosie Andrews Candidate number: 4004 1

The average amount of time taken for 20 oscillations of a pendulum for different lengths of strings Aim: To understand whether the length of a pendulum affects the amount of time taken for it to oscillate

Diagram

Method of the lab experiment Apparatus: • • • • •

Clamp stand Pendulum (string with weight at the end) 2 blocks of wood Stop clock Ruler calibrated in cm and mm.

The independent variable we chose to investigate was the length of the string; this we would change throughout the experiment to learn whether the time taken for 20 oscillations changes. My constants are the mass of the pendulum and the angle from which the pendulum is began. These I will be checking throughout the experiment to increase the amount of accuracy and reliability • • • •

Placed string in between 2 blocks of wood to manipulate the swing into a certain direction, so the string does not circle or go in random directions as this will affect the dependent. Clamped wood in place with clamp stand, and adjusted height Placed a protractor under wood and placed string so it was at a 40 degree angle Released string and started stop clock unanimously, timed the amount of time taken for 20 oscillations 2

• •

Repeated the process six times so it was easier to spot outliers and to work out a more accurate average. Changed the length of the string and repeated all the steps

Method of the animated experiment The website used: http://monet.physik.unibas.ch/~elmer/pendulum/upend.htm On this website is an animated pendulum and I experimented by changing the length of the animated string so it could reinforce or go against the results of my lab experiment • • • •

Chose a length for the pendulum to be released at Started the timer and counted 20 swings then stopped the timer Repeated the process 3 times – more accurate average Changed the length of the pendulum

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Results for lab experiment Length of pendulum (cm) 15 20 25 30 35 40 Length of pendulum (cm) 15 20 25 30 35 40

Time taken for 20 oscillations (seconds) 15.90 15.47 15.53 15.48 18.06 18.15 18.32 18.09 19.88 20.00 19.78 19.82 21.72 22.85 21.57 21.72 22.85 23.43 23.47 23.50 25.28 25.38 24.72 25.14 Time (T) taken for one oscillation 0.777 0.906 0.995 1.098 1.169 1.253

Average (seconds) 15.38 15.47 15.54 18.03 18.00 18.12 19.88 20.00 19.89 21.56 22.35 21.96 23.46 23.50 23.37 24.81 25.03 25.06 The square of the time for one complete oscillation (T2)

0.604 0.821 0.990 1.206 1.367 1.570

Results of animated experiment Time taken for 20 oscillations (seconds) 4

Length of pendulum (metres) 1.00 2.00 3.00 4.00 5.00

Test one 38.60 57.80 70.60 83.40 91.30

Test two 40.60 57.70 70.80 81.70 95.40

Test 3 40.60 57.80 70.80 81.60 91.30

Average 39.93 57.77 70.73 82.23 92.67

Here I can see several anomalous results, these I have highlighted. These anomalous results have probably been recorded from human error; miscounting the pendulum swings. The decision I then had to make was whether to keep them in my results, to not use them in calculating my average or to repeat the test. I chose to repeat the test to make my results as reliable and accurate as possible; keeping them in there will definitely affect the accuracy of my results and using my other results for an average would not produce an accurate average because I have not done as many tests for the animated experiment. This I will look into in my evaluation.

Improved results Length of pendulum (metres) 1.00 2.00 3.00 4.00 5.00

Test one 40.60 57.80 70.60 81.60 91.30

Length of pendulum (m) 1.00 2.00 3.00 4.00 5.00

Time taken for 20 oscillations (seconds) Test two Test 3 40.60 57.70 70.80 81.70 91.40

Time (T) taken for one oscillation 2.03 2.89 3.54 4.08 4.57

40.60 57.80 70.80 81.60 91.30

Average 40.60 57.77 70.73 81.63 91.33

The square of the time for one complete oscillation (T2) 4.12 8.35 12.53 16.65 20.89

Analysis and conclusion From making the graph and analysing it, I can indentify that there is a positive correlation between the length of the pendulum and the time taken for one complete oscillation (as the length increases, the time 5

also increases as a result). The longer the length of the pendulum, the higher amount of time it takes for one oscillation. This is shown on all my graphs, T and T2 for both the lab and animated experiments.

Evaluation After critically analysing both experiments I believe that the animated method is the most accurate. I believe that these results are more accurate because they have a better line of best fit. Although I did do more tests in the lab, my results were far more ranged; this is because the experiment was not as accurate or reliable, due to several factors. Firstly it could have been possible to add some additional force to the pendulum when releasing it; this force could have been applied to some tests more than others. In addition, the tautness of the string would have made a difference; the looser, the less chance of it swinging smoothly (e.g. it could drop and this could affect the swing in some way). Although we did use blocks of wood to manipulate the pendulum into swinging only from side to side, this was not entirely reliable. Sometimes the pendulum would swing in other directions slightly (this would affect the time) this happened more in some tests than others. Finally the angle that the pendulum was released at may not have been accurate because of the parallax error due to the protractor being so small. On the other hand, with the animated method, the pendulum had no extra additional force, it always swung in the same directions, and the length (tautness) never changed in all cases but one the method was completely accurate. The only flaw to this method was the timer. Due to human error, it is very hard to stop the clock exactly at the end of 20 oscillations. This is because the diagram is quite small and it is moving fairly quickly, however this error was also present in the lab experiment, so if I were to do this experiment again, my timing method is something I would want to ‘tighten up’ and make more accurate. For the animated experiment, I would also want to improve by increasing the number of tests done for each one to five; this way I could ignore outliers without having to do an additional test because I would already have enough results for a reliable average. I would also test more lengths- smaller gaps e.g. 1.5m, 2.5m, by doing this, it could reinforce the results either side of it or show anomalous results more easily. It would also help me achieve a better line of best fit. It was very difficult to declare anomalous results in the lab experiment because my results were so varied – making my results inaccurate. However as the animated experiment results were very similar for outliers were very easy to discover. The problem with this was that I had to redo the test again; which took me time, to carry out the test and to recalculate my data. If I were to do this test again I would definitely take more tests for each one as it will give me a more reliable, accurate average, and I would not have to repeat the test. However for the lab experiment my graph shows two outstanding, anomalous results. These are both for the length 15cms, and occur in T vs. length and T2 vs. length I can identify them as anomalous results as they are plotted a significant distance from the line of best fit. I predict that causing these anomalous results are caused by poor method; as I started on 15cms, I was not used to using the equipment or carrying out the experiment, so poor technique was responsible for my anomalous result. I believe that both my results were very reliable, although the animated version more than the lab results. I believe this because if the test were to be taken again, very similar results will be achieved to the ones that I had. As I did several tests for each length to achieve a better average, and my results were all very similar (for each length) this shows that my results are quite reliable. My lab experiment, although the results aren’t as close as close as the others they are still similar; with the two experiments I have proved the same thing (aim: To understand whether the length of a pendulum affects the amount of time taken for it to oscillate) I have proven that it has a positive correlation, so my lab experiment and animated experiment reinforce each other; making my results reliable. Finally, my conclusion ‘there is a positive correlation between length and time taken to oscillate’ is true. Firstly as I have proven that my results are both accurate and reliable this means the plots making the 6

graph are accurate (subtracting the error of not being able to achieve plotting to the nearest tenth or hundredth) and my graphs; both of them, clearly show a positive correlation. In addition the relationship between the length and the time is very obvious; it is very clear and could not be interpreted as anything else.

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