The same factors affect the pendulum on its reverse swing. GPE gained after reaching its highest point in its swing, is converted into KE needed for it to return back to its natural point of vertical suspension. Due to this continuous
motion, the bob creates an arc shaped swing. The movement of the pendulum is repeated until an external force acts on it, causing it to cease in movement. The pendulum never looses any energy, it is simply converted from one form to another and back again.
Before undertaking the final experiment, I will carry out a couple of preliminary experiments to test whether or not my planned experiment will work out all right. I must, however always keep the mass of the bob the same, as this will alter my results.
Below is my table of results.
As you can see, as I increased the length of the string, the time taken for the oscillations increased. This ties in with my prediction. From this table, I could draw the graph below.
From studying the graph, you can see that the line is one of a smooth curve. This would indicate that the time period is not directly proportional to the length of the string. This made me think and question whether or not is was proportional to 1 over period, or the period2. Therefore, I made a table of length and period2, and the results are as follows.
From this, it is not clear what difference it has made, squaring the period, however. If we draw a graph of these results, it is much clearer.
This graph, quite clearly shows a straight line through the origin. This would indicate that the length is directly proportional to period2. Although there are anomalies in both graphs, I can quite clearly say that as the length increases, so does the period.
Whilst analysing my experiment results, I came across a formula to work out how long it takes for 1 period to take place. By multiplying this by five, I can now find out how long it should for 5 periods to take place, and compare these results next to mine.
L in the equation stands for the length of the pendulum, and notice it is in metres and not centimetres, and g is the gravitational force acting upon it. By plotting a graph of my results against the results that the formula brought up, then I can see how much error my results hold. Another observation, is that mass doesn’t come into this equation, so therefore the mass of the bob doesn’t affect the period. Below is the graph for 5 periods2 using the formula.
The table above, as I said, shows how the formula worked out what the results should have been, and below, are the formula results and my results on a graph.
The black line shows my results,, and the formula results, are represented by the red line. As you can see, at the beginning, both results are fairly similar, but as the length gets longer, there is a bigger gap between the results. I think this is down to human error, and it being harder to judge when a period is up, as it swings more slowly, and further.
I think it was a good idea to check whether or not the formula results would deviate from mine much, as it shows how accurate my results were.
Evaluating
The evidence obtained from my experiment supported my prediction that as the length of the pendulum increases, the period increases. This is also shown in my first graph as it displays a smooth curve with a positive gradient. My
method in squaring the period was successful, as I discovered that it was directly proportional to length, providing all other values remain constant. This was shown by a straight line going through the origin (second graph). These results were
encouraging and led me to believe that my proposed method was sufficient for the experiment.
Some of the results were not accurate, as they did not lie directly onto the line of best fit. This could have been due to human error. However, the majority of my results were not far off the line, and therefore, quite reliable. Had there been any anomalous results, I would have repeated my readings even more.
The formula, provided me with extra data, to compare with mine, and showed the errors involved when a human has to start the stopwatch, by his own judgement.
Factors, which may have affected the accuracy of my results, include:
- Error in swinging the pendulum. If I didn’t let it go perfectly perpendicular to the stand, then my results may have suffered.
- Error in measurement of string. To improve the accuracy of this, I could have marked off the points with a pen to ensure they were as accurately measured as possible.
- Human reaction time. Depending on human reaction time, the
measurement period time could have been measured inaccurately, due to slow reactions when setting the stop-clock etc. This could have been improved by involving another person to aid me with my experiment, for a quicker reaction time.
The procedure was relatively reliable, excluding human error, and so I can conclude that my evidence is sufficient to support a firm conclusion that:
As the length increases, so does the period.
If I were to extend my investigation, I would investigate to provide additional evidence to back up my conclusion, for example, changing the mass or angle of altitude. The results gained would hopefully aid me further in supporting
my Scientific Theory. It would also be interesting to investigate how the factors are affected when the Gravitational Field are not what they are on earth, i.e. how would the pendulum swing differently on mars. This is impossible, however, so I wouldn’t actually be able to do it. A better extension, would be to do with investigating and finding out why the formula works, and maybe link it with other formulas such as , or .
Altogether, I believe that I exploited and sufficiently analysed the results that I gathered.
