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Why is it that short buildings respond more to high frequency oscillations while tall buildings respond more to low frequency oscillations?

I would assume that how they react is related to the natural frequency of the buildings so

$$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

To decrease natural frequency, one can add mass ($\sim$ tall buildings) thus it makes sense to state that tall buildings respond more to low frequency oscillations and vice versa. Is this the true reason behind this phenomenon?

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    $\begingroup$ You seem to be modelling a building as a spring-mass system, with all the mass concentrated at one point. Perhaps it would make more sense to model it like a massive string instead of a spring, with one end fixed (and vibrating) and the other free? That way, there would be multiple natural resonance frequencies... $\endgroup$ – Philip May 5 at 15:20
  • $\begingroup$ You are absolutely right, thanks for pointing it out. $\endgroup$ – Monopole May 5 at 15:21
  • $\begingroup$ If this were true, making a short building with high density bricks would be dangerous. What do you think? $\endgroup$ – IndischerPhysiker May 5 at 15:39

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