# Swing Low: Investigate the Motion of a Pendulum

 Do this Science Project with Your Phone!
 Difficulty Time Required Very Short (≤ 1 day) Prerequisites None Material Availability Readily available Cost Very Low (under \$20) Safety No issues

## Abstract

"Swing me higher, Mommy, higher!" Kids love to ride the swings at the playground. The back-and-forth motion of a swing demonstrates the physics of a pendulum. In this experiment, you will investigate the factors that affect the speed and duration of a pendulum's swing, also called an oscillating motion. You can even use your phone and Google's Science Journal app to record your pendulum's movement and determine its period of oscillation.

## Objective

Investigate the motion of a simple pendulum and determine how the motion of the pendulum is related to its length.

## Credits

La Né Powers

Edited by Ben Finio, PhD, Science Buddies

### MLA Style

Science Buddies Staff. "Swing Low: Investigate the Motion of a Pendulum" Science Buddies. Science Buddies, 13 Mar. 2017. Web. 27 Apr. 2017 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p016.shtml>

### APA Style

Science Buddies Staff. (2017, March 13). Swing Low: Investigate the Motion of a Pendulum. Retrieved April 27, 2017 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p016.shtml

## Share your story with Science Buddies!

Last edit date: 2017-03-13

## Introduction

A pendulum is an object, hung from a fixed point, that swings freely back and forth under the action of gravity. A playground swing (Figure 1) is an example of a pendulum. The swing is supported by chains that are attached to fixed points at the top of the swing set. When the swing is raised and released, it will move freely back and forth. The swing is moving due to the force of gravity on the swing. The swing continues moving back and forth until friction (between the air and the swing, and between the chains and the attachment points) slows it down and eventually stops it.

Figure 1. These playground swings are examples of pendulums.

We see pendulums in other areas of our lives as well, such as in long-case clocks, commonly known as grandfather clocks. But pendulums can do more than entertain and help us tell time. Among other applications, they can show that the Earth is rotating! This was done in the mid-1800s C.E. using perhaps the most famous pendulum, Foucault's pendulum. However, pendulums were being used for centuries before this. One of the first known pendulum uses was around 100 C.E., when a Chinese scientist, Zhang Heng, used it to detect distant earthquakes in a device called a seismometer. Today, pendulums have many applications, including measuring local gravity and helping guide ships and aircrafts.

In this science fair project, you will investigate how the period of a pendulum is related to the pendulum's length. A pendulum's period is the time it takes the pendulum to swing back to its original position. In the example of a kid being pushed in the swings at a playground, this is the time it takes the kid to be pushed and then return back for another push. The period of a pendulum is mathematically related to the pendulum's length.

## Terms and Concepts

• Pendulum
• Gravity
• Friction
• Foucault's pendulum
• Seismometer
• Pendulum period

### Questions

• What is a pendulum and what causes it to swing?
• What are some common uses for pendulums?
• How do you think the period of a pendulum is related to its length? Will a longer pendulum have a longer period than a shorter one?

## Bibliography

Introduction to General Physics Concepts:

• Hewitt, Paul G, 2002. "Conceptual Physics," Prentice Hall, IL.

Simple Physics Concepts for Kids:

• Keller, R.W., 2005. "Real Science for Kids: Physics, Level 1," Albuquerque, NM: Gravitas Publications, Inc.

## News Feed on This Topic

, ,
Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

## Materials and Equipment

• String
• Scissors
• Ruler
• Desk or table
• Heavy textbook
• With option 2 in procedure: Large metal washer or other small, heavy object you can use as a weight.
• With option 2 in procedure: Stopwatch
• With option 2 in procedure: An assistant
• With option 1 in procedure: A smartphone to record your data  We developed the instructions in this project using Google's Science Journal app. The app allows you to gather and record data from the world around you with your phone. You can download and install the Science Journal app for free on Google Play. Note that the app requires Android version 4.4 or higher and is not currently available for iOS devices.
• Lab notebook

## Experimental Procedure

Note: There are two different ways to do the experiment. In one method, you will attach your phone to the end of a string and use Google's Science Journal app to create a graph of its acceleration as it swings, then measure the pendulum's period based on the graph. In the other, you will tie washers to the end of a string to form a pendulum and use a stopwatch to measure its period as it swings.

1. Place your ruler so it hangs off the edge of a desk or table, and weigh it down with a heavy book so it does not fall off.
2. You will test pendulums of three different lengths. The exact lengths will depend on the height of your desk or table. For example, you could test lengths of 20, 40, and 60 centimeters (cm).
3. Create a data table like Table 1 in your lab notebook.
Period
Pendulum length (cm) Trial 1Trial 2Trial 3Average

Table 1. In your lab notebook, write down your results in a data table like this one.

### Option 1: Using the Google Science Journal App

Science Journal is an app that lets you record data using sensors that are built into many smartphones, including an accelerometer which measures motion. You can learn how to use the Science Journal app here and how to use the accelerometer here. In this project, you can use the app to record the motion of your pendulum, and then use the data to measure its period.

1. Cut a piece of string that is slightly longer than the first length you want to test (leave enough extra string to attach it at both ends).
2. Tie one end of the string to the ruler.
3. Tape the back of your phone to the other end of the string, as shown in Figure 2. Make sure the phone is upright when the pendulum is hanging straight down. This ensures that the phone's Y-axis is aligned with the string, so it is OK if the phone twists while it swings. Make sure that the final length of the string is correct. You might have to make an adjustment or re-attach the phone to get this right. Figure 2 shows a completed pendulum.

Figure 2. Smartphone taped to pendulum.
1. Start a new experiment, open the Y accelerometer, and switch to graph mode.
2. Start a new trial in your app and pull the pendulum back about 30 degrees. Press the record button and let go of your phone.
3. Let your pendulum swing back and forth for several periods.
4. Grab your phone and hit the stop button to stop recording data.
5. Your data should look something like the graph in Figure 3. Your graph should show oscillations as your phone swings back and forth. You can ignore the spiky part at the end of the graph (this occurs when you grab the phone). Instead, zoom in on the part of the graph that shows clear oscillations (Figure 4).
6. Drag the cursor along the graph to measure the time between two adjacent peaks. For example, the peaks in Figure 4 occur at 5.5 and 6.0 seconds, so the difference between them is 0.5 seconds.
7. This value is half the period of oscillation of your pendulum. So, the pendulum in this experiment had a period of 1 second. This occurs because acceleration in the Y direction is the same at each end of the pendulum's swing—giving two peaks in the acceleration graph per swing of the pendulum's motion.

Figure 3. Example data from the Science Journal app. The x-axis of the graph shows time in minutes:seconds [min:s] and the y-axis is acceleration in meters per second squared [m/s2].

Figure 4. How to measure the oscillation period from a graph in Science Journal. The x-axes of the graphs show time in minutes:seconds [min:s] and the y-axes are acceleration in meters per second squared [m/s2].

1. Repeat steps 3–8 two more times, for a total of three trials with your first pendulum length.
2. Repeat steps 1–9 for your other pendulum lengths. Record all your results in your data table.
3. For each pendulum length, calculate an average period. Do this by adding up the values for your three trials and dividing by three.
1. Use the Create a Graph website to create a graph of your data with pendulum length on the horizontal axis and average period on the vertical axis.
2. How does the pendulum's period change with its length? Is this what you predicted?
3. Does the period stay constant as the pendulum oscillates or does it change over time?
4. What other information can you gather from the graph using the Science Journal app that you probably can not get just from using a stopwatch as described in option 2?

### Option 2: Using Washers and a Stopwatch

1. Cut a piece of string that is slightly longer than the first length you want to test (leave enough extra string to tie knots at both ends).
2. Tie one end of the string to the ruler.
3. Tie a weight to the other end of your string. Make sure that the final length of the string (after you tie the knot) is correct. You might have to make an adjustment or re-tie the knot to get this right. Figure 5 shows a completed pendulum.

Figure 5. An example pendulum experimental setup.
1. Measure the period of your pendulum.
1. Pull the weight of the pendulum back about 30 degrees. It is important to keep this angle the same for each trial.
3. Release the pendulum. Your volunteer should start the stopwatch as soon as you let go.
4. Stop the stopwatch as soon as the pendulum returns to its original position.
5. Record the stopwatch value in your lab notebook.
6. Repeat steps 2.a–2.e two more times, for a total of three trials with your first pendulum length.
2. Repeat steps 1–2 for your other pendulum lengths. Record all your results in your data table.
3. For each pendulum length, calculate an average period. Do this by adding up the values for your three trials and dividing by three.
1. Use the Create a Graph website to create a graph of your data with pendulum length on the horizontal axis and average period on the vertical axis.
2. How does the pendulum's period change with its length? Is this what you predicted?

## Variations

• Instead of changing the length of string, try changing the number of weights attached to the string. Does mass affect the speed of the swing or how long the pendulum swings?
• Try changing the initial angle of the string when you drop it. Does this affect the speed and duration of the swing?
• Try changing the size of the washers. Does this affect the speed and duration of the swing?
• For a more advanced challenge, you can calculate the expected periods of your pendulums using a mathematical equation. To do this, check out The California Academy of Sciences resource About Foucault Pendulums. For each pendulum, how does the average period you recorded compare to the expected calculated period? If they are different, why do you think this is?

## Share your story with Science Buddies!

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.

## If you like this project, you might enjoy exploring these related careers:

### Physicist

Physicists have a big goal in mind—to understand the nature of the entire universe and everything in it! To reach that goal, they observe and measure natural events seen on Earth and in the universe, and then develop theories, using mathematics, to explain why those phenomena occur. Physicists take on the challenge of explaining events that happen on the grandest scale imaginable to those that happen at the level of the smallest atomic particles. Their theories are then applied to human-scale projects to bring people new technologies, like computers, lasers, and fusion energy. Read more

### Physics Teacher

Our universe is full of matter and energy, and how that matter and energy moves and interacts in space and time is the subject of physics. Physics teachers spend their days showing and explaining the marvels of physics, which underlies all the other science subjects, including biology, chemistry, Earth and space science. Their work serves to develop the next generation of scientists and engineers, including all healthcare professionals. They also help all students better understand their physical world and how it works in their everyday lives, as well as how to become better citizens by understanding the process of scientific research. Read more

## News Feed on This Topic

, ,
Note: A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

## Looking for more science fun?

Try one of our science activities for quick, anytime science explorations. The perfect thing to liven up a rainy day, school vacation, or moment of boredom.