Science In Real Life

Today on Science in Real Life we’re going to shake things up a bit with a discussion of oscillation. That may not sound very ordinary, but every time you see something moving back and forth or up and down, that’s an oscillation (the economic indices notwithstanding). In certain cases of oscillation there arises an additional effect known as resonance, which I’ll come to later.

In all the innumerable examples of oscillation we encounter in our daily lives (a pendulum clock, a children’s swingset, etc), 99 percent of them have one thing in common – they are periodic, which is a fancy way of saying the object in question always takes the same amount of time to go from here to there and back again (hobbits named Baggins notwithstanding).

The length of that period of time is determined by the physical attributes of the system in question. For a pendulum, the length of the string and the acceleration caused by gravity tell you how long each swing takes. The mass of the pendulum has nothing to do with it. There is a story of Galileo deriving that relationship by timing a swinging chandelier in a church with his heartbeats. The story is most likely apocryphal, but it illustrates the instructive nature of large swinging objects (Poe’s pit-based pendulum notwithstanding).

It should come as no surprise, then, that oscillating devices formed the basis of timekeeping for, well, quite a long time. As soon as the precision needed to construct them was attained, spring-loaded gears were made that oscillated at the exact frequency of once per minute, or once per second. The latter is the standard frequency unit known as the Hertz, or Hz. Even in the last few decades, as electronic devices began to replace mechanical ones, oscillations have remained center stage in keeping time. Scientists currently define the second in terms of a particular vibration of a electrons in cesium atoms – 9,192,631,770 of them make one second. And you thought your schedule was hectic.

What’s more, the concept of the oscillator finds a wide range of uses in theoretical physics, if I may wax abstract for a moment, as a modeling device. There are many much more complicated processes where, even if there is no actual oscillatory motion, other parameters can be described as undergoing an oscillation. The model can be used in the areas of rotational mechanics, astrophysics, and even electrical circuits (imagine a pool of electrical charge sloshing back and forth between capacitors and you’ll start to get the idea). The simple harmonic oscillator is probably the most commonly used tool in a physicist’s toolbelt (the belt itself notwithstanding).

Now, resonance. As it turns out, when you have something oscillating, it has a special rate at which it “wants” to oscillate – at which the oscillations are much larger and stronger. Let’s say you’re driving an old car, much as I do. Let’s further speculate that this car’s frame has quite a bit of wear and tear on it, much as mine does, so that it’s not as sturdy as it used to be, and maybe the suspension isn’t performing up to ideal standards. The wheels, when the car is in motion, spin – obviously – and therefore bump and jostle the car’s frame in a particular pattern that repeats every time the wheel goes around once (potholes notwithstanding).

Normally this bumping and jostling is just barely perceptible. But like any object, the car’s frame has a resonant frequency, and if the wheel is going at just the right speed to bump the car frame at it’s very special resonance frequency, you might find the steering wheel of this old car juddering and jostling itself under your hands as you drive. Much as I did.

To clarify, in order to have resonance, there must be something driving an oscillation that is itself periodic. Pushing a kid on a swingset once won’t do it, you have to apply a push every time at the back end of the swing. If you do it at just the right rate, the kid starts gaining much more altitude than you could get at any other frequency. Resonance, therefore, is like two oscillations interacting in just the right way so that they are themselves oscillating together. When they do that, they add up to make one much bigger oscillation. So there you have it – the explanation for how things behave when they repeat (parenthetical observations notwithstanding).