How the length of string affects one oscillation of a pendulum.

These sets of results show that there is in fact a significant time range. But when putting the formula into context, this shouldn’t have happened. The acceleration of the object is equal to the total force divided by its mass. This works for both the mass as well as the distance that the string is pulled back. Once again all the results were not close enough/almost identical, proving that once again this cannot be a significant variable.

Length of string:

I kept the distance at which the pendulum was pulled the same as before (30 cm). The only variable that I changed was the distance the length of the string (going up by 5cm each time), making sure it was a fair test. I allowed the pendulum to oscillate 10 times and then divided the time by 10 to work out the average oscillation time, I repeated each test twice and then worked out the average. Here are my results:

There is a great difference between this and the other possible variables; by only changing the length of the string by 5cm there is an obvious but (relatively small) difference of time in 10 oscillations. The reason for this difference is even though gravity has the same effect on all of the weights (so the acceleration will be the same), the distance it has to swing is increased or decreased by the length of string, this causes the time difference between the results. This is the variable I will use for the rest of my investigation. Due to the fact that this was the variable that stood out the most, applying my scientific knowledge cancels out both the mass (a=f-m 2a=2f-2m if you double the mass the force needed doubles these can be cancelled down to result in the original formula) as well as the distance the string is pulled back (if the distance that the string is pulled back is doubled so is it’s GPE)  

I want my results to be as accurate as possible but using the available equipment, it will be hard to have a complete degree of accuracy. In my investigation I will be using:

• A clamp
• Length of string
• Ten gram weights (x5)
• A stopwatch
• A protractor
• A one-meter rule and
• A weight holder.

I will set out the apparatus as below:

Safety will not really be a big issue in these sets of experiments, but I will still keep a safe distance from the pendulum when it is swinging. This is the only real safety precaution I will need to take.

Now that I have worked out which variable I will be using, I will simply follow the steps that I took when carrying out my preliminary test but make sure I take more time and they are more accurate. I will be measuring the time taken for 10 oscillations and then divide the time taken by 10, giving me the time for one oscillation. I will repeat each test twice and then work out the average. To keep my tests fair I will only change the length of the string. I will be using the human eye and a simple stopwatch (goes to 2.d.p) to record my results. I predict that as the length of string increases so will time taken for 1 oscillation.

Method:

I have chosen no safety equipment due to the reasons above in my plan. I have made sure that I have used the same stopwatch each time I did a test; I also used the same weights (there is possibly a small and insignificant difference in mass between the weights). I will be using five 10g weights because this proved the most reliable in my preliminary tests.

Here is how I carried out my experiments:

• I attached a piece of string (roughly 60cm long) to the clamp, making sure it was firmly attached, before hand making a loop for the weight holder, I attached the weights to the weight holder, and the weight holder to the string:

I then twisted it around the top of the clamp until I got to the desired length:

• Using a one meter rule I measured a height of 30cm and pulled the pendulum,
• Then I released the pendulum, and as soon as the first oscillation had occurred I started the stopwatch,
• The watch was stopped after the tenth oscillation and recorded the results in the table below.

Results:

My Graph:

Using my piece of graph paper I have compared the ideal results (using the formula T=2π√ l ∕ g) to my results. Using this method I could accurately compare each individual piece of data. Here are my results:

There is a clear relationship between the length of string and the time taken for 1 oscillation. This relationship is “when the length of the string is increased so is the time taken for one oscillation.” My prediction was correct and on my graph there is an obvious trend. I don’t have the results to say whether or not this trend will ever end (e.g. will the relationship still be occurring when the length of string is 10 meters), but based on the formula T=2π√ l ∕ g the trend will continue. The accuracy of the pendulum was reasonable which resulted in a single anomalous result in my final results (see graph) and another in my preliminary tests (see table in section “Length of String” the anomalous result is the average in the row headed 10). Using the line that the formula has generated I can now comment on the two differences in the lines. The formulated line shows the correct position of the points, showing that all my results were in-fact slightly off. If I were to take an example of one of the points and compare them (24cm) you can see that there is a difference of 0.05 seconds. This is well within the 10% average range showing that my results were accurate.

Conclusion:

This investigation ran a lot smoother than I had expected, with only a few minor inconveniences. The inconveniences wouldn’t have affected my results an awful lot, if at all. The first of the two problems was, the way in which I had tied the knot on. This resulted in the pendulum (instead of swinging in a straight line) it slightly veered to the left, if doing the experiment again I would simply clamp the string in horizontally stopping the shorting and lengthening of the piece of string. The second problem that I encountered was the momentum of the pendulum rocked the clamp. To counteract this I would have simply added weights to the bottom of the clamp. Another mistake that could have caused the anomalous result/s if that I only measured the string before I had attached it to the clamp, causing a tightening and loosening of the string. I chose the best-suited apparatus i.e. I used the most accurate stopwatch available etc. I repeated each test 3 times to clear up anomalous results, and for my preliminary results I felt that 3 results would be sufficient, I also thought that repeating them twice would be adequate. But the anomalous result in my preliminary test (length of string) showed I was wrong. All of the preliminary results were pretty much accurate but throughout the experiment there was a slight variation in repeated result, this could have been due to either equipment or simple human accuracy. I would say that my investigation was not exactly limited. If I were to extend this experiment then I would repeat the experiment either changing the weight of the pendulum, or change the lengths of string that I used, to check wither these variables would change my results.