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I am thinking of making a model of swinging building during earthquake and study the methods to minimize the swinging.

So does it even makes sense to approximate the swinging buildings (the base of the building) to simple harmonic motion? if not then what kind of motion does the buildings do.

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    $\begingroup$ Hmm. This may be more of a question about engineering than earth science. I'm not voting that it's off-topic (I think it's borderline), but others might, and if it is closed then I suggest trying on engineering.stackexchange. $\endgroup$ Aug 9, 2019 at 17:06
  • $\begingroup$ There are already engineering solutions to minimise the swaying of tall buildings during an earthquake. I think they depend on a counter weight, but I have forgotten the details. I also don't know if one has been put severely to the test by a major earthquake, These high tech solutions are a very new thing. $\endgroup$ Aug 9, 2019 at 18:05
  • $\begingroup$ Yes. In fact, in PSHA we use a damped single-degree of freedom harmonic oscillator (with a particular damping and resonant period). E.g., see pdfs.semanticscholar.org/5e13/… $\endgroup$
    – stali
    Sep 12, 2019 at 19:59

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By the definition of simple harmonic motion (restoring force proportional to displacement), no. You need to take into account damping.

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I'd say not simple. Check out my diagram below.enter image description here

If you want to simulate a tall building, I would suggest using a long wooden dowel or thin board, rigidly anchored to a movable base or fairly long metal lever, and move the base (or lever). You could video it at the fundamental and harmonic frequencies, then, playing it back on still frame, count the number of frames per cycle to determine which harmonic(s) it resonates at.

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    $\begingroup$ I think the original question asks whether the ground ("the base of the building") moves as a sine wave. From that input, the response of the building would need to be calculated/measured/observed and would be like your answer. But you did not address the original question. $\endgroup$
    – JohnHoltz
    Feb 1, 2023 at 17:41
  • $\begingroup$ @JohnHoltz I'd say, the ground would act a bit like a transmission line, carrying the wave from the rock movement(s) and it's harmonics, which will be reflected and refracted by the ground surface, and rock density profile. It would become rather complex, but in the tremors I have experienced, it seems to be mainly a sine wave at about 4Hz. I live 80Ks south of Sydney. We've never had it bad. The one that hit Newcastle was barely discernable. I felt a steel ring on a steel floor move. One guy saw cars in a car park dancing, and my wife was told she was mad when she saw the office safe moving. $\endgroup$ Feb 9, 2023 at 3:37

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