To investigate the factors, which affect the swing of a pendulum.

 

Changing the mass of the bob:

Again there does not appear to be any connection between the size of the mass used and the swing of the pendulum. This is because as the height is increased so is the speed however the pendulum has further to travel. Therefore the two affects cancel out and the angle has no affect on the time swing of a pendulum. I have chosen to use a mass of 200g in my main experiment as it is not too heavy as to make it jump but it is not too smaller a mass as to make the weight of the string and hook significant.

   

Changing the Length of the string:

Here my results show a clear pattern. As the length of string was increased the time it took the pendulum to oscillate is also increased. I am therefore going to investigate this further. In order to be able to make a clear conclusion I have decided that it would be best to collect about 10 results.

Hypothesis: I predict that as the length of the string is increased so will the time it takes the pendulum to oscillate. I have seen this in my preliminary experiment but also as I know that the start position and mass don’t affect the swing of a pendulum the length of string therefore must. This is because as it is increased the bob has further to travel in order to complete a swing. As the angle has not changed, neither has the potential energy. Also the force remains the same, as the mass has not changed. So the bob has further to go with the same energy and acceleration. Hence it will move slower and take longer to oscillate.

I also predict that the relationship between these two factors is in some way proportional. This is because I know from background information I found in a textbook the equation for the period of a simple pendulum is:

T=2∏ √L

           g

This can then be rearranged to give the formula:

T²=4∏²L

        g

I know that:

Gradient= y

                x

With this knowledge I can see that:

4∏²   

  g

represents the gradient. Therefore if it were to be plotted on a graph you would get a straight line proving than length and time must be proportional.

I further predict that length and time must be directly proportional as the above formula;  T²=4∏²L  takes the form:

                                g

y=mx+c

As c is 0 the line on a graph would have to pass through the origin making the relationship between the two factors time and length directly proportional.

Information from a textbook relating to my prediction:

Equipment:

• Clamp stand

• 110cm of string

• Meter ruler

• Protractor

• 200g bob

• Stopwatch

• Scissors

Diagram:

Method: After setting up the clamp stand I measured out a length of string, tying a loop at one end to attach the bob to. After measuring out 1m using a meter ruler, I attached the other end of the string to the clamp stand. Next I measured an angle of 20° with a protractor, where I released the bob from. As soon as it reached the central point my partner started the stopwatch. When the bob had completed 5 oscillations the time taken was recorded before repeating the process another two times (with the same length of string). After recording these results in a table I repeated the experiment using a variety of lengths; 100cm, 90cm, 80cm, 70cm, 60cm, 50cm, 40cm, 30cm, 20cm and 10cm. All results were recorded in a table of results.

Safety: In order to make sure that the experiment was safe the pendulum was set up away from where other people were working, to prevent the bob fro hitting them. We also made sure that the surface the clamp stand was on was level and the bob not too heavy, to make sure the pendulum was stable and wouldn’t fall on anyone.

Fair test: To make sure the experiment was fair I changed only the length, keeping the mass and angle the same the whole way through. I also repeated the experiment 3 times for each length in order to make any anomalies more obvious and to allow for an average to be taken for greater accuracy. When measuring the length of string I used a meter ruler to make sure it was correct and a protractor when measuring the start angle. I also made sure that the bob could swing freely without any obstructions, which might slow it down.  

Results:

Conclusion: I can conclude from my results that as I predicted time does increase proportionately to the length. My first graph was not a straight line but did follow quite a regular curve. My second graph however, for time² was as I predicted a straight line, which went through 0 proving time directly proportional to length.

I can see how accurate my results are by using the equation T²=4∏²L  and swapping in my results.                                                      g

                                           

The gradient for my graph of time² against length is

1.0 (sec)  = 3.33’

0.3 (m)

If my results were completely accurate the gradient should actually have been:

4∏²  =  4∏²  = 3.95(2dp)

  g         10

Also I can check my results against gravity, which should equal 10.

1²= 4∏² 0.3     g= 4∏²x0.3      g=11.84(2dp)

        g                      √1

So my result were not totally accurate, although they were not too far out and the degree of accuracy can mostly be accounted for.

Evaluation: Although my results were not entirely accurate they still follow roughly the right pattern. The most likely reason for any mistake is probably an error in timing. This is because it was hard to start and stop timing at exactly the right point and also some leeway must be given for human reaction rate. Another reason for inaccuracy might be that the way the string was attached to the clamp stand, which meant that there was sometimes some friction caused. If I were to carry out the experiment again I would have two people timing so that averages could be taken. Also I would mark the centre point with some brightly coloured card so it was easier to see. I might also take the average of 10 swings rather than five, so that when timing you would have more time to react but also that any timing error would be less significant to the results.