# Period of a Pendulum Lab

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Pendulums have a lot of interesting physics to discover. Try this pendulum lab, investigating the relationship between the length of a pendulum and its time period.

## Introduction

Research Question: How does the length of a pendulum affect the period of that pendulum?

Age: High school

Time to complete: 1 hour

Safety concerns: Very few. Be sure not to position your feet below the pendulum if using a large mass.

Independent variable: Length of the pendulum string.

Dependent variable: Time period of the pendulum.

Controlled variables: Mass & angle of release.

Pendulums might not be super common these days, but the physics surrounding them is fascinating. Things that you might expect to affect the period of pendulum (like mass for example) often don't. In fact there only one or two things that can truly change its period, and one of those is the length of the pendulum. In this lab we're going to investigate the relationship between those two variables.

## Materials

For this physics lab, you will need:

• A pendulum bob or hanging mass
• A ring stand, bar and clamp, or other aparatus to hold the pendulum
• Meter stick
• Stopwatch
• Plenty of string

You may also find useful:

• A long, thin object (which could be a second me to stick) and some tape
• A protractor

## Steps

1. Set up the pendulum so that it hangs above an empty space, such as over the edge of a desk.

2. Measure the length of the pendulum string using the meter stick. Measure from the center of the weight to the point where the string meets its support.

3. Move the pendulum to one side, and prepare to release it at a small angle above the horizontal (5-15 degrees).

4. For consistency, set up a marker behind your desired release point. This can be done by taping a second meter stick or other long piece of wood to the desk. Alternatively, you can strap a jumbo protractor to the ring stand, and use it to keep the angle of release consistent. This is harder to do, but is actually a better choice if one is available to you.

5. Release the pendulum and start the stop watch. This is easiest when working with a partner - one person can release the pendulum while the other starts the stop watch.

6. Measure the amount of time it takes for the pendulum to swing back and forth three times, stopping the stop watch when it returns to the starting point the third time.

7. Note down the time, and then repeat the measurement at least five times.

8. Find the average of your five trials, and then divide that average by three (for the three swings). The number you get is the average time period of the pendulum.

9. Change the length of the pendulum string, and repeat the measurements and calculations. Do this 3-5 times for 3-5 lengths of pendulum. This will give you an average time period for each length of pendulum.

10. Plot a scatter graph with length of pendulum on the x-axis, and time period on the y-axis, and add a line of best fit.

11. If the line is not straight, try the following:

• Squaring the lengths of the pendulum, and plotting those values on the x-axis instead.
• Taking the square root of the lengths of thependulum, and plotting those values.

12. Find the slope of your straight line, and note down the equation which relates the two variables.

13. The ideal slope should be equal to two pi divided by the square root of 9.8 (the acceleration due to gravity). Calculate this number and see how far off your value was.

Troubleshooting:

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