The Effect Length Has on a Pendulum's Period

The Effect Length Has on a Pendulum's Period

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The Effect Length Has on a Pendulum's Period

Prediction:

I predict that the shorter the length of string, the shorter the time
it takes for the pendulum to complete one period. The longer the
length of the string, the longer the time it will take to complete one
period.

Equipment needed for experiment:

-Clamp

-Stopwatch

-Bob/Ball

-Metre ruler

-String

Obtaining the results:

I will be measuring the length of the string in 10s, so that I can
obtain a wider range of results. I will then take 10 readings, and
calculate the average time of osocilation for each length, making it a
fair test. I also need to take into account what factors will affect
this experiment. I need to be very careful when calculating the
length, and make sure I use a ruler.

Method:

- Set up equipment as follows; Attach bob to string. Tie the string to
the clamp leaving a length of 100cm for it to swing from. Make sure
the stopwatch is set to 0 and draw up a table to record the results.

- Hold the bob at a right angle from the clamp stand, and let it drop,
timing how long it takes to complete one period with the timer.

- Do this for all 10 lengths, timing them five times each, so you are
able to work out a reliable average time for each of them.

Time (secs)

Average

Length (cm)

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

10

0.91

0.87

0.92

0.98

0.92

0.92

20

1.06

1.13

1.1

1.04

1.02

1.07

30

1.3

1.41

1.33

1.33

1.35

1.34

40

1.72

1.32

1.4

1.34

1.38

1.4

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50

1.84

1.33

1.7

1.69

1.81

1.67

60

1.7

1.69

1.77

2.03

1.7

2.04

70

1.93

2.13

1.98

1.86

2.28

1.88

80

2.23

2.05

2.02

1.95

1.94

2.04

90

2.29

2.13

2.34

2.25

2.2

2.24

100

2.02

2.34

2.55

2.53

2.41

2.37

Conclusion:

From the results I have gathered I can see that the longer the length
of the string, the longer it takes for the pendulum to complete one
period. This is what I predicted at the beginning of the experiment.

Evaluation:

I think the method I used was a good way of carrying out the
investigation, as it was a fair test. The results were quite accurate,
but could be more accurate by doing an average of more than five
different sets of results. This could also be a fairer test by making
sure the string the pendulum is attached to is exactly 90°
(right-angle) from the clamp stand.

Doing background research into the pendulum I found that Galileo was
the first to properly experiment on this work. He discovered that a
pendulum with a length of string four feet long would have a period
that would be twice as long as a pendulum with a string one foot long.

So if the pendulum had a string that was 40cms long, it would be twice
as long as a pendulum with 10cms.

If the period for a pendulum of 40cms was 1.4, then the time of the
period for the pendulum of 10cms should be 0.7.

I tested this theory with my results and found that it was correct,
though not entirely accurate, It was roughly the same. The reasons for
the average time not being entirely accurate could be a problem with
the stopwatch, and also anything measured in this way is not going to
be 100% accurate.

The results that don’t fit the pattern of the rest of the graph are
called anomalies. An example of an anomaly on my graph could be for
length 60cms. The time suddenly jumps up, but then back down again.
This could be a problem with calculating the average or maybe one of
the trials was extremely off-target.
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