Engineering can sometimes be surprisingly precise. For example, if we know the size of a steel beam and the actual load that will be to be applied to that beam during an in situ load test, we can predict the amount of deflection under load to a few hundredths of an inch. In a case like this, we are dealing with a math problem that was solved centuries ago and that depends only on known data and a few easy-to-satisfy assumptions.
On the other hand, when we are asked to investigate a floor that vibrates under load, we are often reduced to generalizations. Vibrations are obviously a real and measurable phenomenon, but human perception of them is subjective and varies enormously. If a floor sags under static load, the amount of sag can easily be measured and, more importantly for this discussion, is visible to everyone. Some people may feel the sag is more important than others do, but no one won’t see and/or feel it. Vibrations, on the other hand, are sine-wave accelerations perceived, as are all accelerations, through the movement-sensing ability of our inner ears. (Obviously, extreme floor vibrations may be visible as furniture bounces, but this is rarely the case.) People’s sensitivity to acceleration in general, and vibration in this specific case, varies.
Non-subjectve measurement of vibration is based on frequency and amplitude: roughly, how often does the floor move and how fast does it move? A Reiher-Meister-type plot shows the general relation between frequency, aptitude, and perception, although for any given person the thresholds may vary. The following version is from the FAA, discussing when structural vibrations from airplanes are a problem:
GIven that the perception of the problem varies, the efficacy of the various possible solutions vary. We can recommend making the floor heavier, since the energy that goes into moving the floor will now have to move a greater mass and will therefore move it less (smaller amplitude, sometimes lower frequency). This may require structural reinforcing and therefore may be intrusive work. We can recommend stiffening the floor, which has a similar effect but is inherently structural reinforcing, We can combine the two, which is quite effective but also quite intrusive. In short, there’s no simple and easy solution.
