# Period of a Pendulum

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Introduction

PRACTICAL INVESTIGATION: THE SIMPLE PENDULUM

AIM:

The aim is to investigate the factors which affect the period of oscillation of a simple pendulum.

THEORY:

Over 400 years ago, Galileo came up with the theory that the period of a pendulum depends only on the length of the pendulum. A simple pendulum consists of a weight hanging off a string. When the bob is stationary, the two forces acting upon the bob – the tension of the string and gravity – equalise and gives the bob an overall force of 0N. However, when the bob is in motion, the forces are unbalanced and the bob swings back and forth. If the amplitude of the string is increased, the weight will swing back and forth at a regular period. However, if the amplitude of the swing is increased too much, this may cause the weight to bounce and the period of a pendulum may be void. The period of a pendulum is the time for one complete swing. The equation for the period of a pendulum is

T =

where ‘L’ is the length of the pendulum, ‘g’ is the acceleration due to gravity and ‘T’ is the period of a pendulum. However, when doing a practical, the period of a pendulum can be determined by measuring the time a pendulum takes to swing twenty periods and dividing the results by twenty.

HYPOTHESIS:

Middle

23.41

23.87 + 0.82s

1.19 + 0.82s

Length = 32 + 0.2cm, mass = 99.89g + 0.01g

Amplitude of Swing vs Time of a Pendulum

Time for 20 swings (s) | |||||

Amplitude of Swing (cm) + 0.2cm | Trial 1 | Trial 2 | Trial 3 | Average | Period of motion (s) |

4 | 23.16 | 23.59 | 23.43 | 23.39 + 0.23s | 1.17 + 0.23s |

6 | 23.57 | 23.28 | 22.63 | 23.16 + 0.53s | 1.16 + 0.53s |

8 | 21.69 | 23.59 | 23.97 | 23.08 + 1.39s | 1.15 + 1.39s |

10 | 23.75 | 23.69 | 24.00 | 23.81 + 0.19s | 1.19 + 0.19s |

Amplitude = 6+0.2cm, mass = 99.89 + 0.01g

Length of String vs Time of a Pendulum

Time for 20 swings (s) | |||||

Full Length (cm) + 0. |

Conclusion

Again, drawing conclusions from this experiment, it can be seen that the amplitude of the swing does not affect the period of a pendulum. Although there are varying results, no definite conclusion can be draw from the data.

This experiment also shows the length of a pendulum does affect the period of a pendulum. Also, it shows that the relationship between the square root of the length and the period of a pendulum is linear and proportional. This conclusion is very accurate as all the points lie on the line of best fit. The proves that Galileo’s theory was partly correct when he predicted that only the period of a pendulum was only dependent on the length of the pendulum and not on the mass of the pendulum or the amplitude of the swing. This also proves the hypothesis was partially correct when it states that the factor that will greatly affect the period of the pendulum was the length of the pendulum. The part that both theories failed to recognise was that the period of a pendulum was dependent on the square root of length and not the length. This experiment investigated the factors which affect the period of oscillation of a simple pendulum.

Sources:

http://www.8886.co.uk/pendex1.htm

http://cc.ysu.edu/physics-astro/Report.PDF

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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