Methodology
I am first going to set up my apparatus as above over the end of a flat desk so there is space for the pendulum to swing. I am going to do each test three times on each variable (e.g. repeat it three times when the mass of the bob is 100g). I am going to let the pendulum make 20 oscillations for each turn. I will start the timer once the pendulum has passed the centre point. See diagram 1. I will then count one oscillation not when it comes back from when I released it but when it goes through the centre point in the same direction. See diagram 2. I will then carry on counting when it passes through in this direction. See diagram 3. I will stop the timer when it goes through the centre point and will do this on every mini experiment to make it all as fair as possible.
When I am testing on the mass of the bob, I am always going to release the pendulum from the same angle of displacement. I have chosen this angle to be a standard 20° and I will use a protractor to measure this. I will always make sure that the protractor will always be lined up straight. I will also use a standard length of thread of 80cm. I am going to test on 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, 50°, 55°, and 60°. I am going to test at 100g, 200g, 300g, 400g and 500g. I chose to stop at 500 because it would be difficult going any higher as the string will not be able to hold much more weight and also the stand would be unbalanced.
When I am testing on the angle of displacement I am going to use a standard mass of the bob at 100g and the length of the thread at 80cm. I will be using a metre stick to measure the length of the thread. . I am going to test on 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°, 45°, and 50°.
When I am testing on the length of the thread I am going to keep the angle of displacement at 20° and the mass of the bob at 100g. I’m going to test the length of the thread at 100cm, 90cm, 80cm, 70cm, 60cm, 50cm, 40cm, 30cm, 20cm and finally 10cm.
If I find after testing three values in each variable that there is no change I will stop experimenting on it and assume that that variable has no effect on the experiment. This advantage will save me precious time.
Prediction
I believe that the length of the thread will definitely effect the time for a complete oscillation because when the thread is longer, therefore bob has to travel a further distance to complete the oscillation, and all of this slows down the whole process of the swing. I also think that the angle of displacement will effect the time of the swing because if it is held further up then the bob has to again travel further to complete a whole oscillation. I do not think that the mass of the bob will effect the oscillation at all because
Results
Here are the results I found in three separate tables.
Results for length
I have now found that the length does have an effect on the time for a complete oscillation as I predicted. I think that the reason for this effecting the time for an oscillation is because the length of the thread is making the journey for the bob longer and making the whole process slower.
Results for Angle of displacement
I have now found that the angle of displacement does not effect the oscillation of the pendulum, which I did not realise in my prediction, and I now know the mistake I made. In the prediction I mentioned how it would effect the time of the oscillation because the pendulum has to travel further but what I did not realise is that it also travels faster and it must get faster at the same pace as the angle changes so it always ends up taking the same amount of time. I have now learnt from the mistake I made in the prediction.
Results for The Mass of the Bob
I was correct in my prediction in saying that the mass of the bob
Was my experiment accurate?
Now that I know that I know that only the length has an effect on the oscillation I can eliminate the other two now and just see if the experiment on the length was accurate enough.
There is a formula to see if I was accurate: -
T = period
l = length
g = acceleration
Here is a table using the above formula.
From this graph I can see that I performed the experiment fairly accurately. The last one (10 cm) is a little out of accuracy because the pendulum swings much faster so it is also harder to stop and start the stopwatch on time at the start and end.
Another way to see if I performed the experiment accurately is to check the gradient of my graph compared to the gradient of the square root of the length to the time of one oscillation. The closer the difference of the two gradients, the more accurate the experiment has been done. See graph o n next page.
Final Conclusion
I have learnt a lot from doing this experiment and have thought of ways to improve it if I were to do it again. Firstly I would not do the experiment alone. This was the biggest mistake I made because I must have been inaccurate when letting go of the pendulum and starting the stopwatch at the right time. My results were not too bad at all though and I was expecting them to be more out when they were. Another I noticed during the experiment is that I used two different kinds of stopwatches. One of them had an immediate response while the other had a bit of a delayed response because the button was harder to press. If I noticed that it obviously not started on time I redid that part of the experiment but obviously I did not notice every single little mistake I made so that also was a small inaccuracy. What I must realise is that no matter how many times I do this experiment, it will never be done perfectly, being a human it would be impossible to get it 100% accurate with the apparatus available from the school. To get it almost 100% accurate a sensor would be needed but that still would not be perfectly accurate. I have also come to the conclusion that the only way to change the period of a swing is to change its length of the thread or to do the experiment in a different planet having a different value for gravity.
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