# Investigating the Time Period of a Pendulum

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Investigating the Time Period of a Pendulum

The time period of a pendulum is the time taken for the pendulum to
swing from one point to another point, for instance from point A to
point B and back again. This diagram illustrates the experiment.

This experiment calls for me to record this time period, however I
feel it is too short, so I will time 20 time periods for accuracy. I
will then take this number and divide it by 20 to give one accurate
time period.

When doing this experiment I will need to think of two independent
variables:

1. The mass of the pendulum

2. The length of the string that attaches the pendulum to the clamp.

Through my own preliminary experiment I will change the length ten
times, varying from 1m 3cm - 13 cm at approximately 10cm intervals.
For this experiment I will keep the mass the same, the original mass
of the pendulum, 34.87g. For my preliminary experiment when I change
the mass, I will change the mass ten times varying from 74.52 grams to
26.5g. Throughout I will keep the length the same, only changing one
variable at a time. As I mentioned before I will time the length of 20
swings of the pendulum for accuracy.

I chose these figures because I am not experienced in how to control
lengths and weights, which is why some of the lengths are
inconsistent.

Here are the preliminary results

Mass (g) Time Period of twenty swings (s)
1. 74.52 28.53
2. 69.32 28.47
3. 63.31 28.63
4. 57.7 28.53
5. 50.05 28.53
6. 45.01 28.23
7. 43.02 28.13
8. 41.5 28.13
9. 40.02 28.35
10. 36.5 28.43

Length Of String (cm) Time Period of twenty swings (s)
1. 103 39.13
2. 93 37.93
3. 84 36.63
4. 73 33.63
5. 63 30.73
6. 54 28.63
7. 44 26.63
8.

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In my preliminary experiment, I forgot to vary the amplitude to find
out if it affects the time period but I know from my own scientific
knowledge that it does not. However, I also know from our own
scientific knowledge that an only amplitude angle of 10 degrees or
less will make the equation to find the time period work. This made me
decide to set the angle at a constant 10 degrees. In the preliminary
results I also did not realise to divide the time period of 20 swings
by 20 for one time period, I also now know how to control the
intervals and length of the string, so it is not so erratic.

From looking at the preliminary results, one can state the
displacement and mass of the pendulum will have no effect on the final
experiment results. This can also help to predict the final results:

"The longer the piece of string, the longer the time period of the
pendulum"

This will happen because if the string is longer, it will have a
longer distance to travel, so the time period will be longer. The
longer the piece of strings the more potential energy, which will
increase the velocity. From my own scientific knowledge I understand
that the time period of a pendulum (T) equals two pi (2âˆ) times length
in metres (L) over gravity (G).

[IMAGE]

If gravity is at a constant 9.81 N/Kg and the lengths our known, I
should be able to do a prediction graph and table. If our experiment
colludes with the graph, I will know it is accurate and was a valuable
test, information I can use in my analysis and evaluation.

In our final experiment we will use 11 lengths from 110cm to 10 cm,
using intervals of 10 cm. I will use a constant mass as the pendulum,
and the displacement length will be 10 degrees. I chose these values
because the lengths are spread out, to create a fair test. I will time
20 time periods to make it a fair test.

To help make it even fairer, I will repeat the experiment three times
and take an average of the results.

For the prediction table, but not graph, it is helpful to note that as
the equation works only in metres, the values, which would be in
centimetres in my experiment, have been changed to metres.

Prediction table:

Length (m) Gravity (N/kg) Time period (seconds to 2 d.p.)
1. 1.10 9.81 0.71
2. 1.00 9.81 0.64
3. 0.9 9.81 0.58
4. 0.8 9.81 0.51
5. 0.7 9.81 0.45
6. 0.6 9.81 0.38
7. 0.5 9.81 0.32
8. 0.4 9.81 0.26
9. 0.3 9.81 0.19
10. 0.2 9.81 0.13
11. 0.1 9.81 0.06