First of all, can the floor mat be assumed to be a spring? The spring takes in loading gradually instead of taking an impact force. But how does elongating the time duration of a force reduce the noise? Does it have something to do with the frequency of the vibration? In the case of impact force, I assume it is high frequency. In the case of spring force, I assume it is low frequency. But they eventually have the same amplitude of force. What the former case has a higher noise????