I. Pendulum Experiment Instructions (No Measurement version)

Videos (Windows Media Player Format, may not work on Apple machines)

Materials

Setup

The Pendulum experiments were used by Galileo to demonstrate the law of inertia and the equal rate of fall of heavy and light objects. Galileo also discovered the mathematical relationships between the period, the amplitude, and the length of the swing.

I. Varying Amplitude (how far it swings) .

A. Let a pendulum swing for a while and watch it as it wears down. Does it nearly return to the point where it was let go after the first swing? What principle of Galileo’s does this illustrate? Why would Aristotle have disagreed?

As it starts to swing less and less does the period (the time for it return to its starting point) of its oscillation decrease?

Legend has it that he first discovered that the period is independent of the amplitude while watching this lamp in a cathedral in Pisa.

B. Varying the Amplitude and Measuring Period: Video Instructions (These are for the quantitative version)

Start the same pendulum from different heights to make the swing or amplitude greater or less.

Does the period vary with amplitude? Can you figure out why? Why do you think this is important?

II. Varying the length of the string: Video Instructions (These are for the quantitative version)

Try different length strings and see how this affects the period of the pendulum. Does it get faster or slower as the string gets longer.

Can you figure out why?

III. Different Weights: Video Instructions (These are for the quantitative version)

Galileo’s description:

"...repeat many times the fall through a small height in such a
way that I might accumulate all those intervals of time that elapse
between the arrival of the heavy and light bodies respectively at
their common terminus, so that this sum makes an interval of time
which is not only observable, but easily observable." Galileo

"...two balls, one of lead and one of cork, the former more than
a hundred times heavier than the latter, and suspended them by
means of two equal fine threads, each four or five cubits long.
 
"This free vibration repeated a hundred times showed clearly that
the heavy body maintained so nearly the period of the light body
that neither in a hundred swings nor even in a thousand will the
former anticipate the latter by as much as a single moment, so
perfectly do they keep step." Galileo

1. Try releasing two identical pendulums at the same time. How long do they stay together? Why do you think they start to get out of sync?
2. Different weights. Release the heavy nut with the lighter ring clamp, making sure the lengths of the two are identical. Do they stay in sync? How long? What does this show? Why was this result important to Galileo?
3. If you want, try some other pendulums. Do they stay in sync with the nut? What do you think causes the difference in results?

IV. Free Fall

Try dropping some objects of different weights at arms length and see which hit the ground first. You will have some plastic balls, some metal balls, and the metal pendulums. You can also use any other materials you have at hand. Do they all hit the ground at the same time? Can you explain why there are differences? Why did Galileo think the pendulum experiment so much more convincing than this one?

Here is a set of simulations of the Leaning tower of Pisa Experiments from the Nova Site.

Additional Resources:

Here is the Rice University site on Galileo’s Pendulum Experiments