# Aim: To investigate the factors that affect the time period of a pendulum

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Introduction

Aim:

To investigate the factors that affect the time period of a pendulum.

Introduction:

A pendulum is a simple piece of equipment,A simple pendulum, is a weight on the end of a piece of string or wire, which when given an initial push, will swing back and forth under the influence of gravity.

The pendulum was discovered by Ibn Yunus al-Masri during the 10th century, which was the first person to study and document its oscillatory motion.

This diagram shows a simple pendulum and the path that it swings in.

The time period of a pendulum is the amount of time it takes to complete one full oscillation. I need to investigate the factors that effect one full oscillation in the pendulum. After I have done this I can decide which factors to keep the same and which factors to investigate.

Factors affecting the oscillation of a pndulum:

Length of string

The length of the string will affect the oscillation of a pendulum because it means that the pendulum will travel a greater distance in its oscillation. The path at the bottom of the pendulum is like an arc of a circle, with the piece of string a radius. Then according to the circle theorem: C=2πr the circumference will increase as the radius increases.

Middle

30

13.99

14.00

13.95

Angle of release in (o) | Average time for ten oscillations (secs) | Time for one oscillation (secs) |

5 | 13.74 | 1.37 |

10 | 13.86 | 1.39 |

15 | 13.93 | 1.39 |

20 | 13.96 | 1.40 |

25 | 13.88 | 1.39 |

30 | 13.98 | 1.40 |

Conclusion:

From my results I can conclude that the angle of release does not effect the time period of one oscillation. The bigger the angle the bigger the proportion of the circle is taken up by the arc. More of the 360o of the circle is taken up meaning there is a bigger displacement in the oscillation. This in turn increases the time taken for an oscillation.

But if you increase the angle of release you are releasing it from a greater height and therefore increasing the gravitational potential energy.

Gravitational potential = Mass x Gravity x height

Energy

So as you can see from this equation if you keep gravity and mass constant and increase the height you will increase the gravitational potential energy.

From another equation we can see how G.P.E will effect the oscillation.

Kinetic energy = Half x mass x velocity2

G.P.E = Kinetic energy

Mass x gravity x height = half x mass x velocity2

So from these equations you can see that as you increase G.P.E you will in turn increase the kinetic energy.

My graph did show slight differences in some of the readings I think this is because of my measuring inaccuracies with the stopwatch. This would have created slight fluctuations in my results.

Mass of bob:

Method:

1.Apperatus needed for this experiment:

- Clamp Stand
- Clamp
- 400mm of fish wire
- 30g, 40g, 50g, 60g, 70g, 80g Mass
- stopwatch
- protractor
- two wooden blocks

2.We set-up the apparatus as shown in the diagram. I pulled the pendulum taught and raised it to the point of release.

3. I let the pendulum go and at the same time started the stopwatch, I let the pendulum swing ten times before stopping the stopwatch. This technique will reduce the error in starting and stopping the stopwatch.

4. I recorded the time and repeated the experiment three times for each of the six different masses to get a reliable average.

Diagram:

Results:

Mass of pendulum bob (g) | Time for ten oscillations (secs) Test 1 | Test 2 | Test 3 |

30 | 14.34 | 14.25 | 14.38 |

40 | 14.32 | 14.28 | 14.40 |

50 | 14.41 | 14.47 | 14.50 |

60 | 14.53 | 14.50 | 14.55 |

70 | 14.44 | 14.47 | 14.47 |

80 | 14.44 | 14.38 | 14.30 |

Conclusion

Method:

1.Apperatus needed for this experiment:

- Clamp Stand
- Clamp
- 100mm, 200mm, 300mm, 400mm, 500mm and 600mm of fish wire
- 12g Mass
- stopwatch
- protractor
- two wooden blocks

2.We set-up the apparatus as shown in the diagram. I pulled the pendulum taught and raised it to the point of release.

3. I let the pendulum go and at the same time started the stopwatch, I let the pendulum swing ten times before stopping the stopwatch. This technique will reduce the error in starting and stopping the stopwatch.

4. I recorded the time and repeated the experiment three times for each of the six different lengths to get a reliable average.

Diagram:

Results:

Length of pendulum (mm) | Time for ten oscillations (secs) Test 1 | Test 2 | Test 3 |

100 | 7.16 | 7.37 | 7.31 |

200 | 9.74 | 9.84 | 9.75 |

300 | 11.75 | 11.75 | 11.81 |

400 | 13.38 | 13.19 | 13.40 |

500 | 15.10 | 15.00 | 15.11 |

600 | 16.47 | 16.44 | 16.47 |

Length of pendulum (mm) | Average time for ten oscillations (secs) | Time for one oscillation (secs) |

100 | 7.28 | 0.73 |

200 | 9.78 | 0.98 |

300 | 11.77 | 1.18 |

400 | 13.32 | 1.33 |

500 | 15.07 | 1.51 |

600 | 16.46 | 1.65 |

Conclusion:

From my results I can conclude that the length of the pendulum does effect the time period of an oscillation. The path at the bottom of the pendulum is like an arc of a circle, with the piece of string a radius. Then according to the circle theorem: C=2πr the circumference will increase as the radius increases. As the circumference increases the bigger the displacement will be from the starting point and the longer the pendulum will take to return to its starting point.

My results have proved this theory so the length of the pendulum will be the factor that I will investigate in my real experiment.

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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