Investigating pendulums.

Investigating pendulums

Plan

A pendulum is an object suspended from a string or light rod that is able to swing back and forth. It is a device used in such objects as clocks. It is made of a string with a bob attached to the end, this is suspended form a point where the pendulum can swing back and forth. Galileo was the first to make a theory about pendulums. He watched one of the lamps swaying, which was suspended from the ceiling of the church he was in. He noticed that as the size of the swing (arc) got smaller the time of the swing remained the same. He knew this as he timed the oscillation against his pulse. It was Christiaan Huygens that came up with the formula for calculating the period of a pendulum’s swing. One complete swing of a pendulum is called an oscillation. The time for a complete swing or arc is called a period.

We were asked to pursue an experiment with a pendulum. In this experiment I plan to investigate to see if changing the length of the string of the pendulum effects the period of the oscillation. I will do this by measuring the time it takes for ten oscillations, then divide that by ten to find the time it takes for one oscillation. I will do this at ten equally staggered lengths of string. I will repeat the experiment three times at each length of string. I have chosen to do this so I can find the average time, as they will probably vary because of the reaction time of the person timing and other human errors. I think this will improve the overall results I obtain. I have chosen to use a bob of a weight on 30g made of plasticine and to pull the pendulum back 20° from its vertical position to let go each time.

Some of the other variables I could have chosen to investigate are:

The angle of release
The mass of the bob
The number of oscillations timed
The shape of the bob

One of the other variables I could change is the shape of the bob. As things like air resistance can effect the time of a period. I think it would be interesting to see if a flat shape would make any difference to the time of the period. I could also change the force of gravity, as there is a smaller force of gravity on the moon and in different parts of the world, but this would be incredibly hard to carry out. Other variables I could change are the angle of pull back and the mass of the bob. I don’t think the mass of the bob will effect the period of the pendulum as it is not part of the equation so therefore must not have any impact on it. I was also thinking weather changing the equipment would make an impact on the experiment. If we were to hang the pendulum from a pin in the ceiling rather than tied around a circular pole would it make a difference? Also would it make a difference if the bob were made of a different material? Or would it effect the pendulum if the bob were a heavier weight?

Prediction

I think that the length of the string will change the time it takes for one period because of the equation:

___

T= 2π√l/g

The “T” stands for the time for one swing, the “l” is length of the string and the “g” is the force of gravity acting on the object and pi is equal to 3.14.

I see from this that if the length is increased, as all the other components of this equation stay fixed, that the “T” or period of the pendulum must increase. Therefore I ...

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Prediction

I think that the length of the string will change the time it takes for one period because of the equation:

___

T= 2π√l/g

The “T” stands for the time for one swing, the “l” is length of the string and the “g” is the force of gravity acting on the object and pi is equal to 3.14.

I see from this that if the length is increased, as all the other components of this equation stay fixed, that the “T” or period of the pendulum must increase. Therefore I think that as I increase the length of the string the period of the pendulum will increase. So if I reduce the length of string in the experiment, the period of the pendulum will also decrease. I also think that the longer the pendulum swings the shorter the arc will become. I think this is because air resistance will prevent the pendulum swinging all the way back to the original point of release.

Using the equation above I have predicted the results of the experiment:

The reason I have devided the last column by ten is because the lengths of the string are in centimetres and gravity is in metres per second and the units need to be kept the same.

Quantitative prediction

I found that in the predicted results I could estimate the period of a pendulum of any given length if I had the results for one given length’s period.

If I had the period for a piece of string of 10cm, then I could find the time for one oscillation of a pendulum with a length of 20 by this formula:

T (period)=0.63 when l=10 centimetres

So as we are doubling the length we times the period by the square root of 2.

0.63 x √ 2 = 0.89

If you look up at the table of predicted results, 0.89 is the predicted period of a pendulum of a 20cm length.

This formula also works for any length you want to find. You just times the given period by the square root of the number of times bigger the length of string is you want to find the period for.

So if we wanted to find the period if the string was 50cm then we would times the period for one oscillation at 10cm by the square root of 5 because 50cm is 5 times bigger than 10cm:

0.63 x √ 5 = 1.41

As you can see from my table of predicted results, this was also correct.

Fair testing

I will make it a fair experiment by using the same equipment as otherwise it could alter results. Also I am keeping all the variables the same apart from the length of the string, as that is the input variable we are experimenting with. Gravity doesn’t change, the angle of pull back will be kept the same and the number of swings we will time will be the same. These are the controlled variables. If we were to change the number of oscillations we time, it would effect the overall results. This is because the pendulum would slow because of variables such as air resistance over a longer period of time and this would effect the data we get after dividing to get the time for one period. We are also going to keep the person timing the same as different people have different reaction times. We will keep the mass of the bob the same and use the same lump of plasticine throughout the whole investigation. The outcome variable is the time measure for one oscillation as this is what we are measuring as a result of what we have changed.

We have carried out a pulmonary test with a pendulum so that we could see if there were any problems with the way the pendulum worked. We found that we needed to tie the string in a different way because it couldn’t move as freely. We found it was very difficult to keep the plasticine in the same shape I don’t think this will effect the investigation that much. We found that the experiment we had planned was safe and worked well once we had corrected the faults. I think that in the really experiment it will be very difficult to keep all the results accurate as we will be working over a few lessons and we might get bit inaccurate with the way we carry out the experiment.

I will conduct this experiment by using the following equipment:

String
Plasticine
Retort stand
Boss head
Clamp
Protractor
Metre ruler
Stopwatch

1. I will attach the string to the clamp and measure the length of it to the selected length and attach the lump of Plasticine to the end.

2. I will then pull the pendulum back at an angle of 20° from the vertical position of the pendulum and let go.

3. I will then use the stopwatch to measure the length of the 10 oscillations.

4. I will repeat this so that I have three readings for that length and then reduce the length of the string by ten centimetres.

The lengths of the string I am using are 100cm, 90 cm, 80cm, 70cm, 60cm, 50cm, 40cm, 30cm, 20cm, and 10cm, this is the key variable I am testing. I have chosen to stager the lengths in ten centimetre gaps as I think it would then be easy to see differences in the movement of the pendulum and the results. We will be measuring the time of the oscillations with a stopwatch that has hundredths of a second. This will ensure that our results are as accurate as possible.

We will make sure we attach the pasticine securely to the string, as it could be dangerous if it came off as it could hit someone. Another safety aspect we will consider is the stability of the retort stand. This is because in our pulmonary test it was wobbling. We will overcome this problem by putting weights on the base of the stand. We will also make sure there are no obstructions in the way of the pendulum swinging so the results are not effected.

Obtaining data

We carried out the experiment successfully.

Here are the results I obtained from the experiment for 10 periods:

(All the times are in seconds)

We had to repeat the experiment at a length of 40cm, as our result was anomalous. We got a result of 14.56 seconds and the others had an average of 13.19 seconds.

In the experiment I noticed that as the length of the string decreased the pendulum swung faster, just as I predicted. Also when the pendulum was shorter, it started swinging in a circle. This is called circular motion.

Analysing evidence

When I compared the results of my prediction to the results I obtained I could see that they were very similar. They were, at most, a tenth of a second out.

I made a graph to show the difference between the mean time for a period from the three sets of data I collected and the predicted results I calculated.

Conclusion

What I predicted came true. My theory that as the length increased so would the period was proved in this experiment. My other theory that the arc will decrease in size through each oscillation was also correct. We found this was because of air resistance. We did try changing the shape of the bob so it was a flat circle and found it didn’t swing as well as it twisted, but its period was longer. I think this is because it had a larger surface area and this meant it was slowed down quicker because air particles could bump into it more easily. It was also less aerodynamic as the bob we used for most of the experiment was in a rough sphere shape.

I noticed that as the length of the string decreased in even steps, so did the period of the pendulum. This shows me there is strong correlation in the length and time of one oscillation. I can also see this in the graph of the mean time of one oscillation against the length of string. The results are almost in a straight line and almost line up with the line of best fit so this shows me I have been quite accurate. I found that the reason the period increased was because of the equation that I mentioned I my prediction.

Using the length of 10cm when we put this into the equation we got an answer of 0.63 seconds, when pursuing the actual experiment we got an answer of 0.72 seconds. Considering the reaction time of the person with the stopwatch I think our results were extremely accurate, as we were less than a tenth of a second out from our predicted result.

Evaluating evidence

We did come across some problems when pursuing this experiment. We found it quite difficult to control all of the variables. I said I would like to keep the same equipment but that was impossible because we were in different rooms doing the experiments and it took a few lessons and it was impossible to tell which equipment we had used before.

Whilst pursuing this experiment I noticed that when the string was at some of the shorter lengths it began to swing in circular motion. I was not sure why this happened. But it was quite difficult to measure the oscillation as it was moving in a circle rather than an arc, I think this may be why some of our results were not quite what we expected.

I think that another of the reasons that our results were not completely accurate to the predicted results is reaction time. I think that because there is a delayed time in stopping the stopwatch it will alter the results slightly. We were told that most people’s reaction times were about a quarter of a second, but because different people have different reaction times we cannot rely on just this statement. Another element that could have altered our results is our inaccuracies when measuring the angles and lengths of the string. It is very difficult to make the pendulum the same length as the bob changes shape as it is made of plasticine.

I think my results were quite accurate and we only had one result that was extremely different. This was our only anomaly and I think it was caused because we were nor really concentrating and being entirely accurate.

I think my results were reliable enough to draw the conclusion that the length of the string has a big impact on the period of the pendulum. As the length of the string decreased so did the period.

I think this experiment could be made more accurate if we had had more time to pursue it, we would have been more accurate with our measurements. One of the main problems we had with this experiment was keeping the retort stand steady. When the string was at its longest length the stand would wobble. We overcame this problem by putting lots of weights on the base and it eventually worked. I think that if we took more readings at each length then we could possibly draw a better conclusion.