The relationship between a pendulum and g is described in the following limerick:

*If a pendulum's swinging quite free*

Then it's always a marvel to me

That each tick plus each tock

Of the grandfather clock

Is 2 pi root L over g

Then it's always a marvel to me

That each tick plus each tock

Of the grandfather clock

Is 2 pi root L over g

In order to improve the accuracy of my results, I counted the time taken for ten complete 'swings' or periods, and quoted this. I also repeated each ten-swing measurement three times, so that I could take an average and identify any anomalies. And somehow, saying that, I feel like I'm writing up a GCSE science coursework piece!

Here are my results...

length (l, in metres) | 10 swings (10T, seconds) | Run 2 | Run 3 |

0.162 | 8.45 | 8.31 | 8.35 |

0.237 | 10.09 | 9.90 | 10.04 |

0.321 | 11.63 | 11.67 | 11.66 |

0.344 | 12.09 | 11.90 | 12.17 |

0.410 | 12.98 | 12.95 | 13.00 |

0.475 | 14.23 | 14.13 | 14.03 |

I calculated the average value of 10T, and hence T and then T

^{2}, which I can use to determine g, with the following rearrangement:

An alternative, if I'd wanted to plot a graph of my data, is to determine g by finding the slope of the appropriate plot. Using the following rearrangement, it's possible to plot T

^{2}against l and have a slope of 4pi^{2}/gHowever, I'm going at it in number-crunching form, using the formula above. My results for g are as follows:

length (l, in metres) | g in ms^{-2} |

0.162 | 9.136 |

0.237 | 9.338 |

0.321 | 9.332 |

0.344 | 9.3436 |

0.410 | 9.612 |

0.475 | 9.395 |

So, not perfect, but given the nature of the experiment - me with a fireguard and a pine cone - it's not too bad at all, and I feel quite pleased at having worked out something so massively significant with such basic equipment, and I feel it proves that science isn't just for big-budget departments!

Next time, determining the distance to the moon using the same principle as for geostationary satellites (except that this one is a bit bigger, a bit further away and

*not*geostationary!).

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