Swing Low: Investigate the Motion of a Pendulum

Introduction

We see pendulums in other areas of our lives as well, such as in grandfather (also known as longcase) clocks. But pendulums can do more than provide fun at recess and help tell the time—among other scientific applications, they can show that the earth is huge! This is because the swinging motion of a pendulum is due to the force of gravity generated by the earth's size. Other factors, including a pendulum's length, can also affect its motion. 

Background

The time it takes a pendulum to swing back to its original position is called the period of the pendulum. For example, this is the time it takes a child being pushed in a swing to be pushed and then return back for another push. The period of the pendulum depends on the force of gravity, as well as the length of the pendulum.

Materials

• Two identical chairs
• String or yarn
• Ten metal washers of identical size or six pennies
• Strong tape
• Meter stick
• Scissors
• Stopwatch accurate to 0.1 second
• An assistant

Preparation

1. Place the two chairs back-to-back. Space them about one meter apart. Lay the meter stick on the backs of the two chairs, centered on the back of each.
2. Cut one piece of string to a length of 70 centimeters. Cut a second piece of string to a length of 35 cm. Tie one end of both strings to the meter stick, toward the middle of the stick. Space the strings about 20 to 30 cm apart on the meter stick.
3. Tie five metal washers to the free end of each string. Alternatively, if you are using pennies and tape, securely tape three pennies to the free end of each string.
4. Tip: If the meter stick does not seem to stably sit on the backs of the chairs, you can try to tape the ends of the meter stick to the chairs.

Procedure

1. Pull the strings tight (by holding on to the washers or pennies at the ends) and position the strings at the same angle from the meter stick.
2. Have an assistant ready with a stopwatch. Drop the longer pendulum and, at the same time, have the assistant start the stopwatch. Then have the assistant stop the stopwatch when the pendulum returns back to its original position. If the pendulum hit anything as it swung, such as the wall, readjust your setup and try timing the pendulum again. How long does it take the longer pendulum to swing back to its original position? This is the period of the pendulum.
3. Again, pull the strings tight and hold them at the same angle from the meter stick.
4. Have the assistant reset the stopwatch. Drop the shorter pendulum and, once more, have the assistant time the period of the pendulum. How long does it take the shorter pendulum to swing back to its original position?
5. Time the periods of the shorter and longer pendulums a few more times. Are the periods consistent for each pendulum or do they vary a lot?
6. Is the period of the longer pendulum longer or shorter than the period of the shorter pendulum? How different are the two periods? Is this what you expected?

Observations and Results

A pendulum's period is related to its length, but the relationship is not linear. A pendulum that is twice as long as another pendulum does not simply have a period that is also twice as long. The exact periods of your longer and shorter pendulums may be slightly less than 1.7 seconds and 1.2 seconds, respectively, because of friction and because their lengths were less than 70 cm and 35 cm (due to strings being used to tie to attachments).

Perhaps the most famous pendulum is Foucault's pendulum, which showed the earth's rotation in the mid-1800s. One of the first known pendulum uses was in about A.D. 100 when a Chinese scientist, Zhang Heng, used it to detect distant earthquakes in a device called a seismograph. Today pendulums have many applications, including measuring local gravity and helping guide ships and aircrafts.

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