GordMay is absolutely right and many sailors have no idea what the mast pumping is or that this occurs until they spend a significant amount of time on their vessel, usually when they become live-aboards. . Then when they discover the Mast Pumping they think it is a new consition, since they never experienced it before.
With certain winds moving around the mast it tends to want to move or "Pump", no matter what type of rig you have or how tight the stays are. Most of the time mine pumps when the wind is coming from the quarter or stern, so while at anchor
, there is no problem.
As GordMay suggested, hoist a fender (or any other large object) up a halyard
with a tag line on the bottom and secure it so it is against the mast. It will break up the wind and stop the Mast Pumping. Sometimes even large flags
will do the trick.