[adhesive_wombat]

Basically, things that are bolted tightly onto 73 million million million tonnes of rock tend not to flop around very much. It's a near-perfect "momentum sponge".

Things in virtual freefall that can flex (and everything can) do so in response to forces (e.g. thrusting, but also heat stresses, say), and will continue to do so if they start unless you take care to damp them and dump them into heat. There's nowhere for the vibration to "go" unless you design one in. Sometimes the structure of the craft itself has enough damping for practical purposes, especially when you take care to isolate large vibration sources (the ISS has a Sorbothane damper for the treadmill, for example), but when your big floppy (i.e. light) mirror surface has to stay put on a nanometre scale, it's not so simple.

It's a bit like the difference between a tuning fork glued down flat to a table and one hanging from a string.

[pyinstallwoes]

By any chance do you know the history of these solutions and what what went before understanding this or was it already calculated and known far in advance of needing to account for it?

In the sense of building things that last in space.

[adhesive_wombat]

I don't know specifically. I imagine that a lot of the concepts came from naval architecture (sloshing of fuel, water and cargo has sunk many ships through the ages, for example, as well as hull resonances called "springing") then aviation (e.g. "flutter", where the wings oscillate, has destroyed planes) and space and missiles (again with the fuel sloshing, and other modes like pogo oscillation where the vibration feeds back into the engines and self-reinforces). Some concept of it also in civil engineering: the Tacoma Narrows bridge is the canonical example.

Fundamentally they're all somewhat similar in that there's a flexible and/or sloshing thing that doesn't have a huge mass that it's rigidly connected to. Spacecraft deployed in space usually have smaller forces on them (no air or water and the hard acceleration is done) but are also much flimsier due to being ultra-light. Telescopes are even worse as even a tiny vibration can ruin the usefulness of the optical paths.

Vibration of telescopes is an issue on Earth as well, e.g.: https://opg.optica.org/ao/abstract.cfm?uri=ao-53-21-4651