...teams from the Marshall Space Fight Center worked to reassure nervous NASA managers that a further uncrewed flight of the Saturn V was not required, demonstrating on Saturn test articles that their solutions to the Apollo 6 vibration issues would work.
But they didn't. Little known fact that one of the near-misses that came really close to killing the entire crew of Apollo 13 was massive pogo that developed on one engine that was so severe it bent the mountings 24" (yes, inches) vertically out of true. Another few seconds and the first stage would probably have broken up. As luck would have it, for reasons that were and remain unknown, the malfunctioning engine spotaneously shut itself down. IIRC this was /not/ as s result of the pogo - not directly, anyway.
Tons of fascinating detail (and more likely to be correct than my recollections from reading this article years ago) : https://www.universetoday.com/62672/13-things-that-saved-apollo-13-part-5-unexplained-shutdown-of-the-saturn-v-center-engine/