I found the following info as I didn't exactly understand the dynamics even though I had experienced this problem many times while simming.
"Many swept wing aircraft suffer a dynamic instability problem known as Dutch Roll.
Dutch roll happens when the aircraft has relatively strong static lateral stability (usually due to the swept wings) and somewhat weak directional stability (relatively.) In a Dutch roll the aircraft begins to yaw due to a gust or other input. The yaw is slow damping out so the aircraft begins to roll before the yaw is stopped (due to the increased speed of the advancing wing and the increased lift due to the swept wing effect.)
By the time the yaw stops and begins to swing back toward zero slip the aircraft has developed a considerable roll rate and due to momentum plus the slip angle the aircraft continues to roll even once the nose has begun returning to the original slip angle.
Eventually the yaw overshoots the zero slip angle causing the wings to begin rolling back in the opposite direction.
The whole procedure repeats, sometimes with large motions, sometimes witch just a small churning motion. Like all dynamic stability problems, Dutch roll is much worse at high altitudes where the air is less dense.
Dutch roll is almost certain to happen in a jet aircraft is the Yaw dampener is turned off at high altitude. Therefore, the first thing to check if an aircraft begins to exhibit Dutch roll is that the Yaw Dampener is on. The pilot should then try to minimize the yawing oscillations by blocking the rudder pedals (i.e. hold the rudder pedals in the neutral position.) Next apply aileron (spoiler) control opposite to the roll. The best technique to use is short jabs of ailerons applied opposite to the roll. Try to give one quick jab on each cycle (i.e. turn the wheel toward the rising wing, then return it to neutral.) Finally accelerate to a higher speed, where directional stability will be better, or descend into more dense air, for the same reason."
hope that helps


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