If your mast is pumping 3-4 inches, something is definitely wrong. It is the forward and aft lower shrouds that would allow the mast to pump this much. Double check to see that the rig is tensioned properly. In order of the greatest tension to the least, it is the cap shrouds, intermediates, forward lower and lastly aft lowers. Excessive back stay pressure that puts the rig under compression stress could cause pumping as well.
Secondly, check the compression post or bulkhead or what ever it is that is directly below mast mounting plate. This structural member may have rot or cracked over the years.