# Amplitude RMS vs Amplitude in understanding vibration

I am reading this paper, which talks about dealing with mechanical noise.

When characterizing their existing noise, it says the following:

The integrated RMS vibrations up to 1 kHz on the mixing chamber plate are approximately 2 μm in the vertical z direction and 6 μm in the lateral directions x and y.

It seems they integrated noise spectral density.

In implementing some of the mechanical noise isolation technique, what I care about is what the actual, physical size of the total vibration I will have, rather than the magnitude of individual components, which I believe Power Spectral Density represents.

So, I think the integrated RMS is what I am interested. (let me know if I am wrong on this point) But does this figure actually equal the actual magnitude of oscillation? For example, if I bolt an object onto a plate which has an integrated RMS vibrations of 2 μm in the vertical z direction, will it actually oscillate vertically by about 2μm?

What I am having a hard time understanding is their 1kHz integration bound.

Shouldn't one be interested in the integrated RMS vibrations up to the infinity? why stop at 1kHz?

## 1 Answer

The paper says the main source of excitation is the "pulse tube" which has a fundamental frequency of about 1 Hz.

If you look at the plots in section IV, it is pretty clear that the large responses are at low frequency (well below 100 Hz) so there is no point in measuring the response at higher frequencies if there is nothing that is going to excite them.

Looking at the plots, and assuming the authors haven't deliberately omitted something that is happening in the 100Hz - 1kHz frequency range, there probably wouldn't be any significant difference in the measurements from a design point of view if the cutoff was reduced to 100Hz.

Of course if a different mechanical system is subject to noise input that does contain high frequencies (e.g a small internal combustion engine running at 12,000 RPM where the fundamental excitation frequency would be 200Hz not 1Hz) an arbitrary cutoff point of 1kHz would be much too low.

• Thank you for your answer. So, does the integrated RMS vibration, which they claim to be 2 μm, pretty much equal to the distance over which the system will vibrate? – Blackwidow Jan 9 '19 at 22:20