From what I understand, pogo oscillation was already a known problem
for Saturn V rocket's first stage (and likely other stages, not sure)
long before, say, Apollo 11, especially on its central out of 5 main F-1
engines due to, I guess, not sturdy enough support structure
(cruciform) and the central engine's force moving it upwards, shortening
the fuel line during high thrust and vice-versa when the engine was
off.
It might have been a known problem even before the first Saturn V
flight. They (von Braun et al.) were dealing with combustion
instabilities that they were trying to solve (or at least establish
where the problem is) by adding a small explosive charge to the engines
assembly and detonating it during hot fire testing of the first stage
engines. That didn't go too well, and this pogo oscillation problem
persisted at least also for the first Saturn V flight of Apollo 4.
