Preliminary results
According to scientific theory, the relationship between varying the length of string and the time period should be:
Using the formula I can predict that (results are recorded in seconds):
- 20cm of string will be = 0.88
- 40cm of string will be = 1.26
- 60cm of string will be = 1.54
- 80cm of string will be = 1.78
- 100cm of string will be = 1.99
These results do not correlate with my practical preliminary results. I believe that gravity was not given to an accurate enough measurement. Therefore I will change gravity from 10 to 9.8 - a more accurate measurement. I hope that my results will match now.
These new results match much better and shows how being as accurate as possible will produce a much firmer conclusion.
Full practical result table
These results were taken using a simple pendulum as shown in an earlier diagram.
These results are all measured to 2 decimal places. The average column is rounded to 2 decimal places as you cannot improve accuracy by finding the mean.
A table to show the difference between the formula results and the experimental
My results get more accurate as the string is lengthened but there is only one result which if I could I would repeat: the last one as it is 0.2s out. All my results are fairly accurate and from the table I can see that they become increasingly accurate with longer lengths of string. This degree of accuracy will surely bring me to a firm conclusion.
How I can use the graph
From the graph I can see that no result was correct to 2 decimal places. The experiment was conducted under poor conditions relying on human reaction times. Human reaction times, I believe, are responsible for all the results being higher then the formula results. Overall, the results were good bar the one which I have circled and the rest are accurate to one decimal place.
From my graph, it easy to find any formula or experimental results, using the lines of best fit.
e.g.
Formula experimental
Length of string 47cm time = 1.4s 1.46
Length of string 33cm time = 1.16s 1.24s
Formula experimental
Time period 0.44s length of string = 7cm 6cm
Time period 1.78s length of string = 80cm 75cm
Why to use a graph?
This method of working out times and length from a graph is far easier and quicker then using the formula. Unfortunately, on the graph I used the scale was too large and did not provide very accurate results. This can be altered through changing the scale of the axis.
Explanation of the time increase
The length of string quite obviously affects the time taken for one complete oscillation, but why?
The longer the length of string the longer the time taken for one oscillation as I predicted but what I didn’t predict is that the range of time between each result would get smaller. This is shown not only in the table of results but also in the graph as it has a curved line. The reason why the time length is getting bigger is that the distance the suspended weight must cover is getting larger as demonstrated in the diagram below.
Analysis
My graph and results back up this explanation. Also my initial prediction was similar, this is enough evidence for a strong conclusion. This is true as my results correlate with that of the formula, also on my graph they produce a smooth steady curve with no jolts or abnormalities bar one, which I have already recognised and ignored in the line of best fit. Furthermore, my results on their own produce a pattern strong enough to suggest that there will be a formula, and most certainly, the length of string does affect the time taken for one complete oscillation.
Evaluation
Once again I believe that the experiment produced enough correlating and pattern data to make a firm conclusion. This is due to testing 18 different lengths of string and recording 54 times to two decimal places. What makes me more confident is the fact that the results correlated with the proved and tested formula and that the results produced a smooth curve on the graph. All this evidence produced did not contradict each other but worked together to direct me to a firm conclusion.
My results were accurate as I had already improved on my method from the preliminary results and had found it was more accurate to work in a team with one person timing and the other releasing the mass.
There are ways of improving this experiment. The one I believe would make most difference is eradicating human error and placing this responsibility upon machines as the human reaction time is poor and is only reliable to one decimal place. Also to take more results at closer intervals over a wider range of length would be sensible to see how the times progressed. Also conditions for the experiment to take place could be improved in a more controlled environment not a crowded school classroom.
There were three irregular results for one particular length: a 100cm. These showed not to correlate with the formula and were out of place on my graph. This is a good sign that irregularities are clear, as my results are very accurate. This is the only result that needs extra attention and to extend the experiment I would repeat this particular length.
To extend the experiment I could change any of the other variables suggested in my plan. Such as weight or shape of mass. These would create a wider more advanced knowledge of how a simple pendulum works.