The interesting history of stretchy and swingy

Now that's what I call a pendulum
(chaotic pendulum from Dice World)

Not surprisingly, science writers tend to focus on the exciting stuff. Apart from anything else, we get a lot of the less shiny bits at school, and most of us probably don't want to hear any more. You don't get far doing a popular science book on pendulums, say. But this is a bit of a shame, because science writing isn't just about explaining concepts, it's also about context, and the difference between the 'facts' of school science and the fuzzy reality of science as it truly is. So let's take the plunge.

Two favorites of the physics world are springs and pendulums, both examples of objects that undergo regular motion. Galileo is supposed to have first considered pendulums while watching a lamp swinging on a chain at Pisa cathedral. Up to then, no one had thought about the significance of a pendulum’s swing, because their ideas of motion were based on the ancient Greek concept of objects trying to get to their “perfect” place, the center of the universe. This was used to explain why items fell to Earth. But it didn’t help with something that oscillated like a pendulum.

What Galileo noticed, timing the swinging lamp with his pulse (possibly bored in a sermon), was that the time a pendulum took to swing wasn’t linked to the distance the object on the end of the pendulum travelled. Whether it made a long stroke or a short stroke, the time it took was the same. It didn’t depend on the weight on the end of the pendulum either, just the length of the string. At least, that's what they tell you at school. In fact this only applies to relatively small swings and goes out of the window for bigger ones. Galileo had a lot of interest in pendulums and inclined planes as they gave a way to study falling under gravity in a controlled way - despite the legend, the chances are he never dropped balls off the leaning tower of Pisa.

Pendulums were a breakthrough technology in making accurate clocks, but clockmakers soon found there was a problem – metal pendulum arms changed in length with the room temperature, and this resulted in variation in the timing (the swing wasn't small enough). This was overcome by using materials that don’t vary much with temperature, or by using a complex pendulum called a gridiron that linked bars of different materials whose expansion countered each other.

Springs also provide a regular, oscillating motion, provided they aren’t pulled too far. Springs (and anything else elastic, like a bungee) have a limit called the elastic limit. Pull them further than this and they transform permanently. Instead of returning to their original length when released, past the elastic limit they deform. But when springs are kept within the limits, they work according to a simple ratio discovered by Robert Hooke, one of Newton’s contemporaries. Hooke discovered that the further you stretch a spring, the more force you get. Double the stretch, double the force. Technically it’s a negative force because it goes in the opposite direction to the stretch.

Robert Hooke was on the receiving end of a barbed comment from Isaac Newton. Newton said in a letter to Hooke, “If I have seen further it is by standing on ye shoulders of giants.” This sounds modest, suggesting that Newton built on the work of others, and it is often how the quote is used. However, Hooke had a deformed back that made him seem small in stature. No one could accuse Hooke of being a giant and it seems that Newton, whose certainly despised Hooke, was getting his revenge.