King of the swingers

Well, the pendulum has helped to change the world. The story goes that in 1583 when Galileo was still a student, he noticed that a lamp swinging from the ceiling in Pisa cathedral kept constant time even though the swings got smaller over time. He is supposed to have done this using his own pulse as a timer. Whether or not the story is true, Galileo did go on to investigate the properties of the pendulum.

He found out that the period (time for one complete swing) depends only on the length of the pendulum and not on its mass. So that, for example, a one kg and a 100kg bob have the same period as long as the string is the same length. This finding always surprises students, even today, when they carry out the experiment for themselves.

How does the pendulum conserve energy?

A pendulum moves with harmonic motion. It is a good device for illustrating the conservation of energy. When lifted up to one side we give it gravitational energy, when released this turns into movement energy as the pendulum swings downwards. After reaching its lowest point the pendulum slows down as it moves upwards again - movement is now being turned back into gravitational energy, and so on.

This would continue forever if the pendulum was swinging in a vacuum. However, most of the time the pendulum swings in air and so it slowly loses energy due to air resistance. This lost energy is in the form of heat. This means the swings get smaller, but importantly, the period stays constant. This is shown by the two graphs. Notice that they always reach the midpoint of their swing at the same time even though one is being damped.

Putting the pendulum to work

Galileo was the first person to think of using a pendulum to make a clock. However, he was unable to get it working properly. It wasn't until 1657 that a Dutch scientist called Christian Huygens managed to build the first working pendulum clock. He wanted to do this so that ships could navigate more reliably across the oceans. Ships could easily find their latitude (north-south position) but they need to know the exact time in order to work out their longitude (east-west position).

Sadly, Huygen's clock didn't perform accurately at sea, and it was left to an English clockmaker called John Harrison to eventually solve this problem with his marine chronometer, the H-4, in 1760. Harrison's story is one of intrigue and betrayal. In the end, it took the help of Sir Isaac Newton to get the recognition (and reward money) he deserved. Anyone interested in knowing more about Harrison's struggle should read Dava Sobel's brilliant book Longitude.

Pendulum clocks use coiled springs, slowly falling weights or batteries to slowly deliver energy to the pendulum to overcome the damping effect of the air. But there is a limit to how small a pendulum can be made. Most modern watches and clocks use the regular vibrations of a quartz crystal to keep time.

In fact, time is now the most accurately measured physical quantity, using vibrations of caesium atoms in atomic clocks. One second is now defined as the time it takes the caesium atom to vibrate 9,192,631,770 times.

Also, in 1851, the French Physicist Foucault used a 67m long pendulum with a 28kg bob to show that the Earth is spinning on its axis. If observed over the course of a few hours the pendulum can be seen to be passing over different points on the floor tracing out an intricate pattern. This can be explained by the Earth spinning beneath it as it swings.

So how, exactly, did the pendulum change the world? Well, it gave us accurate time across a whole country or region, so that commerce, travel, work and sadly war, could all be coordinated more efficiently. Perhaps most importantly it solved the 'longitude problem', which greatly increased international trade. Today we take for granted knowing the time in our region to an accuracy of one second or less. But in reality this is the product of nearly 500 years of innovation - the first and most important step of which began with the pendulum.