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Gallery 2

# Pendulum Snake

Pendulums of different lengths swing differently to create some fascinating patterns.

## How it works

Gently tilt the board to release the different sized pendulums into a swinging pattern. Watch as the pendulums swing in random patterns of motion, then form a winding snake-like form before randomising again.

## Things to try or ask around the exhibit

• How many times does the snake pattern form?
• Which pendulum swings the greatest number of times?
• Do you think a pendulum influences its neighbouring pendula?
• Which pendulum stops swinging first?

## Background

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.

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.

## Finding the science in your world

The length of a pendulum and its period (time taken to swing back and forth once) is important for equipment such as old fashioned pendulum clocks and metronomes that 'beat' back and forth at a certain pace to allow musicians to gauge timing when playing music.