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What affects the time period of a pendulum.

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What affects the time period of a pendulum


I have been asked to investigate what affects the time period of 1 oscillation of a pendulum.

Definitions: Oscillation: Repeated motion of pendulum (to and for)
Period (T): Time taken for one full oscillation


I predict that the longer the length of string the longer it will take the pendulum to complete one period. This is because the length of the arc, the pendulum is traveling along is greater, but the gravitational acceleration will remain the same. This prediction is also proved by the formula


Here if the length of the string is increased (L) then that side of the equation becomes larger because the size of the fraction is increasing and because one side of the equation is increasing so must the other to remain equal so T will also increase.


What a pendulum is:

A pendulum is a body suspended by a fixed point so it can swing back and forth under the influence of gravity. Pendulums are frequently used in clocks because the interval of time for each complete oscillation, called the period, is constant.

The GPE (gravitational potential energy) 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 loses any energy, it is simply converted from one form to another and back again. However in our experiment an external force of friction is applied in very small instances.

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Measure the string to the desired lengthPlace string on centre of bobWe then pulled the string back to 15 degreesWe then released the bob and started the stopwatch at the same time.We let the bob swing backwards and forwards 10 timesWe then stopped the pendulum swinging and recorded the times.We repeated the experiment with the same length 3 timesWe then repeated steps 1-6 for string lengths 10cm, 20cm 30cm, 40cm, 50cm


Errors in Measuring/Judgment: In many cases we found that when we repeated the experiments, we found that the time or the amplitude was different. This was because every time we did it there was a margin or error. Nobody in the world could ever measure it and get it right with your bare hands. We therefore took the results by averaging the result from three repeated tests so that we won’t get one very strange result from one particular area. We could not measure very accurately either. Many times when a person measures it again, we found that it was often different by 1-3mm. So we will be comparing all results by showing the true time mathematically by the sum: T= 2π √(l/g).

Preliminary Work

To confirm that the theory’s are correct we performed some preliminary experiments using different variables.

With a small bob at 29 cm’s it come to 1.189 seconds for one swing. With a heavier bob it came to 1.207 seconds, so the weight doesn’t affect it, as proved in the theory. The difference between the previously mentioned results was because of unavoidable human error.

However with the small bob with a short string it took 0.929 seconds compared to the long string which took 1.207 seconds.

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the majority of my results were no more than a decimal place away from the
formula results and, therefore, quite reliable. Had there been any anomalous
results, I would have repeated my readings.

Factors which may have affected the accuracy of my results include:
- Error in measurement of angle of altitude. This angle proved difficult to
measure and it was hard to get the exact same angle for each result. To
improve the accuracy of this measurement, I could have attached the
protractor to the clamp stand so that it was in a fixed position.
- 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 stopwatch 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:

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.

I could also investigate the effects of what changing the gravitational field energy would do. I could investigate further whether the formula I found is correct by having the GPE as a factor.

I have heard that the angle the bob is released at affects the results after 15degrees. I could investigate this, and if what I have heard is true, then it would render the equation image00.png to be false.

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