The Physics
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Opus in profectus

# Resonance

## Discussion

Radio transmitters (including television transmitters, satellite uplinks, and cellular phones) broadcast at or near a particular frequency. We are swimming in a sea of different radio frequencies from both natural and artificial sources. How does your radio (television, satellite dish, or cellular phone) select the correct frequency from among all the others for decoding?

Even as a boy, I observed that one man alone by giving these impulses at the right instant was able to ring a bell so large that when four, or even six, men seized the rope and tried to stop it they were lifted from the ground, all of them together being unable to counterbalance the momentum which a single man, by properly timed pulls, had given it.

Galileo Galilei, 1638

This needs to be paraphrased. "An example of how local soil conditions can greatly influence local intensity is given by catastrophic damage in Mexico City from the 1985, MS 8.1 Mexico earthquake centered some 300 km away. Resonances of the soil-filled basin under parts of Mexico City amplified ground motions for periods of 2 seconds by a factor of 75 times. This shaking led to selective damage to buildings 15-25 stories high (same resonant period), resulting in looses to buildings of about \$4.0 billion and at least 8,000 fatalities."

Driven harmonic oscillator

The amplitude of a driven harmonic oscillator increases as the driving frequency approaches the natural frequency. In an undamped system, the amplitude will be infinite.

 A = 1 x = ω = f √((1 − x2)2 + 4γ2x2) ω0 f0

Fall of the Broughton suspension bridge, near Manchester (1831)