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### The Time Period for a Simple Pendulum

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Length: 756 words (2.2 double-spaced pages)
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The Time Period for a Simple Pendulum

A pendulum is a device consisting of an object suspended from a fixed
point that swings back and forth under the influence of gravity.
Pendulums are used in several kinds of mechanical devices, such as
clocks. In the simple pendulum, which oscillates back and forth in a
single plane, all the mass of the device can be considered to reside
entirely in the suspended object. The motion of pendulums in clocks
closely approximates the motion of a simple pendulum.

Aim: -
======

My aim is to find out if the mass on the pendulum affects the time
period of the pendulum.

Key Variables: -
----------------

The key variables are: the mass on the end of the pendulum

the length of the string

how far away from the stand the pendulum is swung from.

Chosen Variable: -

My chosen variable is the mass on the end of the pendulum.

Dependent Variables: -

The dependent variables are: the length of the string

how far away from the stand the pendulum is swung from.

Fair Test: -

In order to keep my investigation a fair test, I will keep all the
dependent variables the same, only changing my chosen variable. I will
also keep the number of oscillations the same.

Prediction: -
-------------

I predict that as the weight increases the time for one oscillation
will decrease. This is because I think that a heavier mass will create
a greater pull on the pendulum, therefore causing the time period for
one oscillation to decrease.

Apparatus: -
------------

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I am going to take five readings for each mass, divide the number by
ten to find the time taken for one oscillation and then find an
average for the five results in order to make my results as accurate
and reliable as possible.
--------------------------------------------------------------------

Preliminary Work: -
-------------------

Mass

(grams)

Time for 10 oscillations (secs)

Time for 1 oscillation

(secs)

Average

(secs)

2

14.75

1.475

14.59

1.459

14.83

1.483

14.78

1.478

14.84

1.484

1.48

10

15.20

1.520

15.26

1.526

15.18

1.518

15.20

1.520

15.19

1.519

1.52

20

15.31

1.531

15.28

1.528

15.59

1.559

15.45

1.545

15.49

1.549

1.54

50

15.51

1.551

15.58

1.558

15.59

1.559

15.58

1.558

15.63

1.563

1.56

100

15.53

1.553

15.69

1.569

15.65

1.565

15.61

1.561

15.71

1.571

1.56

200

15.33

1.533

15.41

1.541

15.49

1.549

15.59

1.559

15.59

1.559

1.55

See graph paper for graph of preliminary results.

Analysis
--------

My preliminary results showed that there was hardly any difference in
the time period for one oscillation, using different masses.
Therefore, I decided to find out the constant for a simple pendulum
from my results.

The equation for this is:

T=Ö l / g 2p

As seen on my graph, there is only a slight change between all the
results, therefore showing that the mass on the end of the pendulum
has no effect on the time taken for one oscillation.

This can also be proved through the use of the equation above. This is
because mass is not included in the equation therefore must have no
effect on the time taken for one oscillation.

The average of all my results is approximately 1.55 secs for one
oscillation, which means that T should also be approximately the same.

So,

T=Ö l / g 2p

T=Ö 0.6 / 9.8 x 2p

T=0.2474356 x 2p

T=1.554683726

T=1.55 secs (2dp)

This is also shown on the graph on the next page.

Originally, I predicted that as the mass increases the time for one
oscillation decreases. However, from my preliminary work I found that
mass has no effect on the time taken for one oscillation. Therefore, I
found the equation for the constant to find out if my results fitted
the equation. From substituting the relevant information into the
equation, I found that my results do fit to the constant; therefore
proving that mass has no effect on the time period for a simple
pendulum.

Evaluation
----------

It is obvious from the graphs, results table and the equation that the
mass on the end of a simple pendulum has no effect on the time period
of the pendulum.

The investigation was successful and there were no anomalous results.
My results are fairly accurate although there may be a slight error in
stopping the stop watch, whether or not the string was the right
length every time and whether or not the pendulum was swung from the
same height every time. Apart from these slight errors, my results are
fairly accurate. These errors may also have affected whether or not my
investigation remained fair throughout.

Due to the amount of results taken and the lack of anomalous results,
I think that my results are reliable. From my results, I was also able
to come to a sufficient conclusion for my investigation.

If I were to do this investigation again I would make several changes.
Firstly, I would probably make sure that my chosen variable had an
effect on the investigation and secondly, I would make sure that my
investigation was more accurate. I would by making sure that the
string is at the exact height every time, making sure that the
pendulum is swung from the same height every time and by being more
accurate in stopping the stopwatch.

MLA Citation:
"The Time Period for a Simple Pendulum." 123HelpMe.com. 20 Apr 2014
<http://www.123HelpMe.com/view.asp?id=120462>.