Last month, I wrote about vibration isolator frequency, and why we have to pay attention to it when isolating rotating machinery (especially in highly-sensitive settings). That discussion centered around the notion of tuning between the spring and the machine it supports. This explains why -- in vibration-sensitive labs and fabs -- neoprene mounts are probably a terrible isolator choice for a 900RPM fan. Here, the isolation frequency is too close to the primary fan vibration frequency; they're "tuned" to each other, and the isolator acts like an amplifier instead of an attenuator.
It's worth pointing out that other tunings can happen, too. And they can be equally problematic. Not only can the isolator be tuned to the machine frequency; the system could also end up tuned to the natural frequency of the structure itself.
You can think of these systems from two different directions. That earlier post looked at the machine isolation problem of a vibrating payload isolated from a sensitive structure. Now, however, let's invert the problem and say that the structure is the vibration source while the payload is sensitive; imagine an optical microscope sitting on a lab bench. The Principle of Reciprocity insures that all the same concepts apply to both.
In our microscope isolation system, the same kind of problematic tuning can arise. If the structure's natural frequency matches the isolated system's natural frequency, then we're going to have problems.
Imagine that you're installing a microscope in a lab, and you choose mounts that result (via pad stiffness and microscope mass) in a 12Hz system resonance. That means that if you bump into the microscope, the entire isolated system will "ring," bouncing back and forth 12 times per second. What if the laboratory is on an upper floor of the building, and the structure -- unbeknownst to you -- also exhibits a natural frequency at 12Hz?
Every time someone walks by, that 12Hz floor resonance is going to get excited greatly; since your isolation system is itself tuned to 12Hz, all that vibratory motion very efficiently finds it way into the microscope. In fact, those vibrations will end up getting amplified rather than attenuated, and your images are probably going to get a lot worse. The same thing would happen even if the frequencies aren't so perfectly aligned; the common wisdom is that the frequencies have to be separated by at least 40% to avoid strong interaction.
So, even when you're isolating microscopes rather than machines, frequency still matters. I didn't choose 12Hz randomly; that's a common number for rubber-type mounts, and it's also common for vibration-designed laboratory floors. So, this isn't just a theoretical risk.
Everything has a natural frequency: the structural floor, the lab bench, the vibration-isolated system. Even the microscope itself has internal resonances; these are the reason why the instrument is sensitive to vibrations in the first place. And when it comes to vibration isolation, allowing these resonances line up (in frequency) is usually not what we want.