The Physics Philes, lesson 86: Does It Resonate?

Unfortunately, last week’s DDoS attack prevented you from getting your weekly dose of physics. But now we’re back, baby, and ready to finish off our discussion of periodic motion.

If you’ll recall, we started out by talking about a very idealized model of an oscillating body. We’ve gradually been complicating that picture by looking at what happens the amplitude is damped.

But oscillating bodies aren’t universally destined to slowly come to a halt. If a force is applied, we can maintain a constant amplitude. Specifically, this will happen if we add a force that varies with time in a periodic or cyclic way. This force is called a driving force and we call the resulting motion forced or driven oscillation.

Every oscillating body has a natural angular frequency. It’s the angular frequency of the oscillating body when it is displaced from equilibrium and then left alone. However, in a forced oscillation, the natural angular frequency is equal to the driving angular frequency.

For example, think about a sinusoidally varying wave. We’ve seen experimentally that when there is only a little damping, the amplitude peaks sharply as the driving angular frequency nears the natural frequency. As the damping increases, the peak becomes smaller and broader until there hardly a peak at all.

This phenomenon has a consequence. It’s called resonance. You’ve probably heard of this. We see resonance in sound and electric circuits. One famous example of some rather disastrous resonance is soldiers walking in step across a bridge. The Mythbusters even did an episode on it.

Another famous example is the Tacoma Narrows suspension bridge.

As you can see, it basically waved around like a ribbon before it fell apart in 1940 and is usually sited as an example of resonance driven by wind. But that might not be quite true. Instead, it might have been something called self-excited oscillation, which means that the wind displaced the bridge further from equilibrium when the bridge was already moving away from equilibrium. Mathematically, it’s basically the opposite of a damping force, so you can understand why it was so destructive!

That’s it for periodic motion! We did it! Don’t worry, though. There is plenty more physics on the way. Next week we’ll start fluid dynamics. Should be fun!

Featured image credit: Wikipedia

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