Pendulum Snake

Start all the pendulums swinging and watch as they resolve from a random pattern of motion into a winding snake-like form. Then watch them randomise again, only to reform into the snake! It’s all done using common factors.

Explanation

Each of the swinging balls is a pendulum that swings back and forth at a slightly different rate, determined by the length of string supporting it.

The longest pendulum swings 15 times in 30 seconds, the next longest swings 16 times in 30 seconds, and so on, until the last pendulum, which swings 24 times in 30 seconds.

Since every pendulum completes an exact number of swings in this time, they all come back together every 30 seconds.

After 15 seconds, the even-numbered pendulums have completed an exact number of swings and are back where they started. The odd-numbered pendulums are exactly halfway through one of their swings and are opposite where they started. The result is two opposing lines of pendulums that seem to dance with each other.

Extras for Experts

You can try exploring highest common factors (HCFs) using Pendulum Snake.

The highest common factor of a set of numbers is the largest integer that divides all the numbers without any remainders.

Let’s call the pendulum that swings 15 times in 30 seconds “pendulum 15”, the pendulum that swings 16 times in 30 seconds “pendulum 16” and so on.

Pendulum 15 and Pendulum 18 have a HCF of 3. They swing together 3 times in 30 seconds.
Pendulum 18 and Pendulum 24 have a HCF of 6. They swing together 6 times in 30 seconds.

Calculate some HCFs between pendulum pairs and test your calculations by counting the number of times they swing together in 30 seconds.

Note that HCFs are also known as greatest common divisors.

Things to Try

Rest the pendulums behind the short clear plastic screen if you want to study only a few pendulums at once.
Make your own mini-pendulum snake at this website!
http://www.exo.net/~donr/activities/Pendulum_Snake.pdf

Questions to Ask

Have you ever tried hypnotising a friend using a pendulum? What are some other things you could do with pendulums?

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