Like I said earlier, the Vertical Stabilizer controls the vertical axis. When the aircraft lost it, it went into a condition of "positive static instability" The engines aggrivated that condition.
The oscillations were from wing forward/rearward pivoting on the center of gravity of the fusalage.(witnesses reported the wings as moving rapidly forward and backward from the ground before it broke apart)
Oscillations will increase in magnitude and frequency when positive static instability is present.
(Just basic physics 101) The engines fell off because the struts could not handle the stress the oscillations......