A spec characterizes the vibration stability by acceleration noise density
$$Na < \dfrac{1\text{ μg}}{\sqrt{Hz}}$$
for 1-100 Hz, where g=9.8 m/s2. But usually what I see is something like 3.5 nm pk-pk.
My question is, how to convert these two?
I tried this as below, but not sure if it's correct, any comment is appreciated.
Displacement noise density (is this correct?)
$$Nx = \frac{Na}{4\pi^2f^2}$$
Thus
$$\begin{align} x^2 &= \int (Nx)^2 df = \int \frac{(Na)^2}{16\pi^4f^4} df \\ &= \frac{(1\mu g)^2}{16\pi^4} \int_{1}^{100} \frac{1}{f^4} df \\ &\approx 2 \times 10^{-14} m^2 \end{align}$$