This explanation was taken from : Basic Facts Physics, by Eric Deeson (Collins GEM.) pg 147
The Period is independent of the amplitude - Galileo claimed that the pendulum period was independent of the amplitude in Two New Sciences. Scholars debate whether he meant that the periods are exactly the same of that they differ very little. As a test of whether they are exactly the same, two pendulums with identical lead bobs were suspended 28.9 cm. They were released at the same time from different angles. One was pulled back about 5 degrees while the other was released from about 45 degrees. The pendulum pulled back five degrees was allowed to travel through thirty cycles, and the numbers of oscillations of the other pendulum during this time were counted. The data is below.
The pendulum which travelled through the larger angle had a longer period. It averaged 29.42 oscillations during 30 swings of the other, and had fewer oscillations in every trial. Clearly, pendulums with different amplitudes do not have the same period. In fact, it appears that pendulums with larger amplitudes have longer periods. The difference is quite small, though. Whether Galileo's claim is true depends on interpretation of the claim, but the interpretation that identical pendulums of different amplitudes have periods independent of amplitude is false.
Hypothesis
I think that when the angle is increased the time of the period will still stay around about the same time. I think this because as the pendulum drops it will get faster, and then will slow down when going back up. So therefore because there is a section when the pendulum is travelling fast and when it is travelling slow it roughly will even out.
Risk Assement
Masses hitting people – I will have to keep my equipment in a corner which will not affect people walking pass.
Masses dropping on someone – I will make the hole powerful enough to hold 400g.
Apparatus
Plan
- First of all set up all the Log IT equipment.
- Then get a clamp stand, masses, string/wire and a protractor.
- Set up all the equipment together.
- Make sure that the string/wire is 25cm long.
- Log on to the computer and start the Log IT program.
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Then adjust the calibration, also change the graph type so that on the y – axis it shows between 50o and –50o.
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Then measure the angle to the first angle that you are going to test for (10o, 20o, 30o, 40o, 50o).
- Re – do the test for each angle three times.
Variables
Mass (200g)
Length of string (25cm in the actual investigation)
Angle of the swing – This is the variable that I’ll be testing.
As you can see, I am changing the angle of the pendulum which it will be let go from, to see if it changes the period of a pendulum. I will have to keep all of the other measurements the same to keep it a fair test.
Fair Testing
I am changing the angle of the pendulum which it will be let go from, to see if it changes the period of a pendulum. I will have to keep all of the other measurements the same to keep it a fair test.
Here is a table to showing my measurements to the nearest accuracy.
Results
Analysis
My graph does show a positive correlation but it does not show very clearly because after the first two values all the values are the same. The values that are values plotted on the graph do not have a very large difference but on the graph it does look like a very large difference. I think that the values of the results are really close together; I had also said this in my hypothesis that the results would come out to be really close. This is because as the angle gets higher the rate of acceleration will increase (this is as it is going to the centre), but then it will slow down as the pendulum goes back up. So therefore when the angle is smaller it will not accelerate as much but then take as slow down as it goes it up, this is because it has a less distance to travel. The fact is that if they are at different angles their time difference for the oscillation will be around the same but with a bit of a difference, as also shown in my results.
Evaluation
The results that I have collected not exact, when measuring the number of swings and the time it took the time was not exact. I think that if I had calculated my average period not to twenty seconds but to the exact time then I would of got some different results. During my practical there was no such difficulty that I encountered which have cause anomalies or any uncertainties.
Bibliography
Book Title/Web address Author and Page
Basic Facts Physics Eric Deeson pg 147 (Collins GEM)
