# Investigate the factors which affect the period of one swing (oscillation) of a simple pendulum.

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Introduction

Pendulum

Aim: To investigate the factors which affect the period of one swing (oscillation) of a simple pendulum. The factors I will use are length of the string, and angle that the bob is released from.

Hypothesis:

1. Length of string

I think that the length of the string directly affects the period of one oscillation. The mathematical formula used to describe the period of the pendulum is:

T= 2π√/g

T is the period (time for one swing - seconds)

is the length of the pendulum (metres)

g is the acceleration dues to gravity. (N/KG)

(Length) is in the formula, clearly indicating that it is a factor which will directly affect the period of time.

To see whether the time period will increase or decrease when the length is increased, I will substitute the formula for numbers to see the result.

Length 0.3, g-force = 9.8N/KG

T= 2π √/g

T = 2π √0.3/9.8

T = 1.009s

Length 0.4, g-force = 9.8N/KG

T= 2π √/g

T = 2π √0.4/9.8

T = 1.269s

The calculations above show that when the length of the pendulum is 0.3m, the time for one oscillation is 1.009s. When the length is increased, the time is increased. When length is 0.4m, time period is 1.269s.

This tells us that when the length is increased, the time period is increased.

2. Angle of release

A simple pendulum is only a weight known as a “bob” hung from a string. When the bob is lifted, the pendulum gains potential gravitational energy, as it is acting against the force.

Middle

The statement α T can be justified by taking values from the graph, for example when the length of the string is 5cm T= 0.481 and when the length is doubled to 10cm T= 0.651, which shows T is almost doubled.

The table below shows actual results compared to the theoretical by working out the percentage error by this formula, percentage error= (actual error (actual result- theoretical results)/ exact value (theoretical results)) x 100:

Length of string (cm) | Theoretical prediction | Actual results | Percentage error |

5 | 0.449 | 0.481 | 7% |

10 | 0.635 | 0.651 | 2.5% |

15 | 0.777 | 0.862 | 11% |

20 | 0.898 | 0.877 | 2% |

25 | 1.004 | 1.014 | 1% |

30 | 1.099 | 1.129 | 2% |

35 | 1.187 | 1.221 | 5% |

40 | 1.269 | 1.267 | 0.2% |

45 | 1.345 | 1.328 | 1% |

50 | 1.419 | 1.489 | 5% |

My average percentage error is 3.6% which suggests that our results are fairly accurate.

Experiment 2

By looking at the results obtained from my graph I found that the angle of amplitude did affect the period of oscillation, however in a very slow rate. Also I found some anomalous results in this experiment which could have been because we did not follow one of our control variables.

Experiment 3

By looking at the table and graph obtained from my results I found that by increasing the mass of the bob had no effect to the period of one oscillation. This could be because that since the gravitational acceleration is 9.8N at all time (on Earth); the mass of the bob will have no deciding effect on the period of oscillation. The reason for this can be taken from my prediction, which is:

Height = - cos θ

Conclusion

- Theoretical Prediction

Planet | Gravitational Field Strength (N/Kg) | Time period (T) (s) |

Mercury | 4 | 2.22 |

Venus | 9 | 1.48 |

Earth | 9.8 | 1.42 |

Mars | 4 | 2.22 |

Jupiter | 26 | 0.87 |

Saturn | 11 | 1.34 |

Uranus | 11 | 1.34 |

Neptune | 12 | 1.28 |

Pluto | 4 | 2.22 |

Deep space | 0 | Infinity |

- By looking at the table I can now base my results on a sound prediction and say that the stronger the gravitational field strength is of a planet the faster the time period is of one oscillation and the weaker the gravitational field strength the slower the time period of one oscillation.

- I cannot continue this investigation, since my school does not have the resources for me to experiment on other planets.

This controlled-falling system is a weight (bob) suspended by a string from a fixed point so that it can swing freely under the influence of gravity. If the bob is pushed or pulled sideways, it can't move just horizontally, but has to move on the circle whose radius is the length of the supporting string. It has to move upward from where it started as well as sideways. If the bob is now let go, it falls because gravity is pulling it back down. It can't fall straight down, but has to follow the circular path defined by its support. This is "controlled falling": the path is always the same, it can be reproduced time after time, and variations in the set-up can be used to test their effect on the falling behaviour.

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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## Here's what a star student thought of this essay

### Response to the question

This is a good essay that ties experiment and theory together quite well. The student has answered the question of what factors affect the time period of an oscillation well. He has at first looked at his theory to determine ...

Read full review### Response to the question

This is a good essay that ties experiment and theory together quite well. The student has answered the question of what factors affect the time period of an oscillation well. He has at first looked at his theory to determine that length will likely determine the time period, and he has also used his initiative to think that angle and mass may affect the time period even though the theory says they do not. He has made a prediction based on his theory and on his intuition, however I would of recommended rather than just going on intuition he should of checked his theory to see what the theory predicts would happen in terms of increase in mass and increase in angle.

### Level of analysis

The student clearly lays out his method which I would recommend always doing as it is best to know what you are doing before you do it, you don't want to be confused as to what to do when you get to the experiment. He calculates all his errors which is very helpful as it both adds depth to the coursework and helps to stop you from making incorrect conclusions, as you can see if the results could be due to errors. However he works out the error by comparing it to how the theory predicts the result should be, you should not do this. Make sure to calculate errors the regular way. He uses theory to calculate why the speed is not determined by the mass of the bob, which adds a lot of depth. However it could have been done easier by realise that the force is determined by the mass, but so is the acceleration, therefore since F=ma, since F is the mass multiplied by another value, you can put the equation as mk=ma, and the mas cancel. You could go into more depth and determine what determines k.

### Quality of writing

The student's grammar and spelling is fine and so is his layout. However he should of made repeats and calculated an average to increase reliability, and he should of made a table for each of his experiments. He could of also plotted a graph to determine how his variables are proportional to each other.

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Reviewed by jackhli 28/02/2012

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