Resonance: the same force, at a different rhythm
A structure can survive a brutal blow and come down under gentle pushes. What decides it is not the force: it is how often it arrives.
What you are looking at
- The green arrow is the force, and it is always the same size. The only thing that changes throughout is how often it pushes.
- The curve on the right draws itself as the rhythm sweeps: it is the map of how much the structure responds at each frequency.
- The building and the curve are the same number. When the dot climbs the peak, the building shakes — these are not two animations, but one.
01The swing already taught you this
Pushing someone on a swing is the whole experiment. Push at random moments and not much happens: sometimes you help, sometimes you brake.
But push just as they come back and every push adds to the last. Within a few cycles the swing is flying, and you never pushed harder.
02Everything has a rhythm of its own
Anything that can oscillate has a natural frequency: the rhythm it swings at on its own if you strike it once and let go. It depends on its stiffness and its mass, not on who is pushing.
A tall building has one. A bridge has one. A wine glass has one, and it is the note you hear when you run a finger round the rim.
03When the two rhythms line up
That is when the response takes off. In the animation the force never changes size, and the amplitude goes from almost nothing to several times more purely because the rhythm approached the natural one.
What keeps the peak from running off to infinity is damping: the fraction of energy the system dissipates each cycle. With low damping the peak is tall and narrow — dangerous and hard to avoid; raising it flattens the peak.
That is where the engineering lives: not in making the structure stronger, but in shifting its natural frequency or taking energy out of the motion.
Where this is used
The damper in Taipei 101
A 660-tonne sphere hung near the top, rigged to move against the building and steal energy from the motion. You can go and see it: resonance made into an object.
Breaking step on a bridge
Troops are ordered to stop marching when crossing a bridge. Marching is, precisely, applying a periodic force — and the bridge has its own rhythm.
Your microwave oven
It emits at a frequency that shakes water molecules efficiently. Resonance used in your favour: the same phenomenon that brings down a bridge heats your lunch.
Tuning a radio
Turning the dial tunes a circuit to resonate with one frequency and not the others. Of all the waves passing through you right now, the set amplifies only one.
Explaining it to a child
The idea, in plain wordsTo make a swing fly you do not have to push harder: you have to push at the right moment. Everything has its right moment.
- Go to a swing. Have them push at random moments: the swing moves little, and jerkily.
- Now have them push always at the same moment, just as the swing comes back towards them. Watch it climb on its own, with no harder pushing.
- Without a swing: hang something from a string and move your hand side to side. Find the hand rhythm that makes it swing widest: there is only one.
The question to leave them withIf everything has its own rhythm, what would happen if a lot of people jumped together, always in a bridge’s rhythm?
For the classroom
Ten minutes with the animation, ready to take into a room. Free under CC BY 4.0, like everything else here.
- Hang something from a string —a key, a pencil case— and ask someone to make it swing as high as possible without touching it, only by moving the hand holding the string.
- Have them try first moving the hand very fast, then very slowly, then hunting for the right rhythm. The difference is dramatic and needs no explaining.
- Play the animation. Now the frequency axis of the curve means something: it is the map of what they just found by trial and error.
- Lengthen or shorten the string and repeat. The rhythm that works has changed: that is the natural period.
Why are soldiers told to break step when crossing a bridge?
Answer: Because marching in time delivers energy always at the same rhythm, and if that rhythm matches the bridge it adds up. Walking out of step delivers the same total energy but mistimed, and much of it cancels.
A singer shatters a glass with her voice. Would shouting louder at any note do it?
Answer: No. It has to be that glass's own note. More volume at a different note is just noise — the point is timing, not intensity.
An earthquake flattens one building and leaves its neighbour standing. They took the same shaking. How?
Answer: Because their natural periods differ. The one that fell was in tune with the rhythm of the ground; its neighbour was not. It is why a building is protected by making it softer, not stiffer.
The answer you will hear is "because the sound was very loud". It is worth not dismissing it: ask what would happen if they shouted just as loud at a different note. That usually opens it up on its own.
FísicaEterna classroom guide · CC BY 4.0 · fisicaeterna.cl
Take it with you
The animation is yours to use: in a class, in a video, in a course. Just credit the source.
Embed it on your site
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The code behind it
It is written in Remotion, which renders video by writing React. The bar and the number are not drawn next to the figure: they come out of the calculation on the same geometry you are watching. If the drawing lies, the number lies with it.
Licence
This animation is under CC BY 4.0: you may copy, redistribute, adapt and use it commercially, as long as you credit the source.
Suggested attributionResonance: the same force, at a different rhythm — FísicaEterna (fisicaeterna.cl), CC BY 4.0