How do earthquakes of different strengths affect buildings of different heights?

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?

• 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... – Philip May 5 at 15:20
• You are absolutely right, thanks for pointing it out. – Monopole May 5 at 15:21
• If this were true, making a short building with high density bricks would be dangerous. What do you think? – IndischerPhysiker May 5 at 15:39