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# Investigate the time taken for a pendulum to oscillate through one time period.

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Introduction

Nelesh Patel 11SB                                          Physics Coursework

Pendulum Investigation

Aim

To investigate the time taken for a pendulum to oscillate through one time period.

## Introduction

We are carrying out this investigation to look at the energy transfer involved in the swinging of a pendulum. A Pendulum moves in a harmonic motion, we can tell as firstly the pendulum moves in a straight line, also if there are variable forces acting on the pendulum and if the force of the pendulum is proportional to the displacement of the mass.

We are also doing this investigation to find out the time taken for a pendulum to oscillate through one time period. A time period is a full oscillation of the pendulum as shown in the diagram on the left, where the pendulum starts at point 1 and swings to point 3 and return back to point 1, this is a full oscillation because it is the movement from one height to another and back again. The purpose of this is so we can look at the factors that affect the time period and then use that factor as a variable in the experiment.

Apparatus

We need the following apparatus for this investigation as shown in the diagram

• Clamp Stand -  To raise the pendulum off the floor and allow a longer string to be used.
• Clamp – To Hold Boss
• Boss – To hold 2 small pieces of wood
• 2 square pieces of wood -  To hold the string that hold the pendulum
• Pendulum -  To investigate the time period of one full oscillation with a certain string length.
• Stop Watch – To calculate Time Period for 1 oscillation
• Protractor – To measure displacement
• Ruler – To measure length of string

Middle

0.4

1.27

0.5

1.42

0.6

1.55

0.7

1.68

0.8

1.79

0.9

1.90

1.0

2.01

The graph is not good enough to be used because our hypothesis states that the time period should be proportional to the length so is we wanted to calculate the time period easily we would just need the length of the string.

I will now try to make a graph with t² against length

 L/m T/s T²/s² 0.1 0.63 0.40 0.2 0.90 0.80 0.3 1.10 1.21 0.4 1.27 1.61 0.5 1.42 2.01 0.6 1.55 2.41 0.7 1.68 2.81 0.8 1.79 3.22 0.9 1.90 3.62 1.0 2.01 4.02 The is what I predict my experiment results will look and when I compare the 2 graphs I should get a very close match. If not then my Hypothesis in wrong.

Fair Test

To keep this a fair test, we must ensure that the string length is accurate, the angle of displacement is same through out and to make sure that reaction time make as minimal effect as possible by measuring the time for 10 oscillations instead of 1.

Safety

There should be no safety precautions as there is nothing heavy or explosive or in anyway harmful being used.

Method

Firstly the apparatus shown in the diagram is set up.

Conclusion

T = 2∏√(l/g) is accurate and works and can be used to work out the time period for any string length of a pendulum swinging in a harmonic motion This graph shows that the relationship between t² and the length of the string is proportionate, this means that the time period is determined on the string length of the pendulum. It shows us that t is not directly proportionate to length as also shown in the prediction graph.

The gradient is 1.1s²/30cm which is 0.34s²/cm. The reason for this connection is because the formula is not dependent on the 2∏ and g because we have shown that

t is proportional √L and so t² is proportional to L.

This proves my hypothesis is correct and that t² and L have a direct correlation and that string length will increase time period and the larger the length is the larger the arc of displacement.

Evaluation

Apart from the 3-4% error margin and the difficulty of obtaining an exact string length to the nearest centimetre, we had very accurate results.

Because of this our results where very uneven but they were not that bad and were still useful.

I think that the data shown in the results and analysis show that my hypothesis was correct.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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