The relationship between the period of a pendulum and its length

In this lab, we will continue our explorations of the gravitational field using one of the simplest physical systems studied as far back as in Galileo’s day: a mass hanging from a string, aka a pendulum. In addition to measuring the gravitational field , we will also be trying to determine the relationship between the period of a pendulum and its length. The basic relationship is

Where

• is the period – the it takes for a pendulum to swing out and back to its starting position in seconds
• is the length of the pendulum in meters
• is the gravitational.

You can see that, like Kleiber’s Law, this relationship takes the form of a power law. The period is related to a constant and the length all raised to some power .

Why do we want to measure again?

You have already measured in prior lab(s). Why would we want to measure it again. Well, the pendulum provides an independent method of measuring which we can compare to our measurements made by dropping objects. In a future lab, you may learn how to compare these two results.

Another goal of this lab – multiple sheets in a workbook

In this lab, you will be expected to turn in a single spreadsheet workbook. A workbook is a collection of different spreadsheets all linked together. Using multiple sheets can help keep all your data organized. Moreover, formulas can reference data on other sheets making a powerful “data analysis program.” The complete workbook for this lab will be significant. However, having all the structure in place will be helpful if and when you need to revisit this experiment to improve upon it. Throughout this lab, we will be guiding you through creating such a powerful workbook: you will really be taking your spreadsheet skills to the next level!

Some terminology that we will use throughout this lab

• Oscillations – Instead of measuring the period for a single back-and-forth, a more reasonable thing is to measure the time for several oscillations and then divide. For example, you could measure the time for five oscillations and then divide by 5. You will determine the number of oscillations to use.
• Trials – In order to reduce statistical uncertainty, we will want to several trials, each of multiple oscillations. For example, you may do three trials of five oscillations each. You will determine the number of trials using the running-average method described in a previous lab.
• Lengths – In order to fit our data, we will need to measure multiple lengths for our pendulum.