You will find in this note, that most vibration problems, and most earthquake disasters, are caused by bizarre resonances.
Everyone thinks they know what resonance is, but they don't really. As the Inuit have many words for snow, followers of Haroldology have many made-up terms for resonance. The simplest is a 'ringing bell resonance'. You tap on the bell and you hear a nice tone, but you can't tap more on the bell, and get the sound louder. You can really whap the bell and get a loud tone, but this is a non-amplifying resonance. The effect can only be noticed if the bell can ring for a long time without energy loss, a tiny crack in the bell deadens it immediately.
This type of resonance makes pretty sounds, but rarely ever causes any problems. Nevertheless, I have seen many types of problem resonances that are analyzed with the inappropriate physics of the 'ringing bell'.
Destructive resonances always involve a self-tuning source. I call this 'swing resonance', since it is similar to pushing a kid on a swing. If you just randomly pushed at the kid with your eyes shut, she wouldn't go anywhere, and would give you the 'He's hopeless!' look. If you had the handy-dandy accelerometer that I want for Christmas, then you would be measuring a spectral peak at the main swing frequency (fundamental mode). But, nothing for the little wildcat.
But Dad's are smarter than that, and you start pushing at just the right frequency. You need very little energy, and soon she is yelling 'Higher, Higher!'. If the swing did not have non-linear damping, you'd soon be wrapping the little monster around the upper bar. Luckily, other forces, such as air resistance, and a tired old man, save her.
With your accelerometer on the swing, you see the final amplitude is hundreds of times greater than the input.
The world is full of swing resonances, with some ending up in massive damage.
(whew! not enough ad money, will continue later)
ps. I'm tired, coming back from Montreal water polo. Filled up a lot of bottles of wine at the giant self-serve vats. Bought cheap beer at the Costco. Luckily, I have sons and relatives who will take care of a lot of it for me.