In layman's terms how much random vibration is 0.75 grms?

Answer 1

grms is not a unit of expressing vibration and thus this is not a valid question. Random vibration is that field of study where the input load to a mechanical system is not deterministic in nature, so we need to analyse it in a probabilistic sesnse. In many situation this may serve the purpose as in many cases we are interested in the peak values of the response and the filed of random vibration enable tackling this in terms of knowing the excitation from the probabilistic sense, i.e. through the knowledge of mean, varience etc.