Mast pumping is caused by the velocity of the wind causing the formation 'vortexes' (rotors) being shed by the geometry of the mast; and, when the frequency (rate) of the vortex shedding is in 'tune' with the natural frequency of the mast, the mast will (can) vibrate in a (destructive) harmonic response to the shedding of these 'rotors' being generated.
This is the vortex phenomenon: Kármán vortex street - Wikipedia, the free encyclopedia
..... and includes a moving diagram/illustration of the event.
This is a 2-part phenomenon - the vibration characteristics of the mast PLUS the action of the wind. To remedy, the easiest way is to change the physical aspects of the mast ... changing its mass/weight, or changing the 'stiffness' of the mast so that one changes the natural frequency of oscillation of the mast, the vibrational characteristics (natural frequency) of the mast is the easiest to control/remedy:
The most common methods or remedy/prevention are:
1. Pre-bowing the mast or adding a forward bend or bow by rigging tension - usually 3/4" forward bow for a single spreader set, or 1/2" forward bow per each spreader set for multiple spreader masts. Such pre-bowing radically
changes the apparent 'stiffness
' of the mast, which changes its 'natural' frequency.
FWIW - all sailmakers expect
that all masts are set up with this pre-bow when they design mainsails as this 'expected' bowing is always incorporated in mainsail design.)
For setting up proper
mast 'pre-bow' or 'pre-bend' go to: http://www.riggingandsails.com/pdf/selden-tuning.pdf
2. Changing or adding mass (weight) to the mast (a temporary solution) -
The raising of any additional large mass/weight up to about mid-span of the mast ... can be any 'heavy' object that stays 'attached' to the mast.
3. adding a 'spiral' of rope/line about the mast - changes the regular pattern of vortices being shed from the mast. Good for when at a dock, slip, etc. ... a temporary solution.
Importance of remediation - such oscillations 'can' mathematically become severe when in complete 'harmony', and can begin by 'impact considerations' exceed the metallurgical limits of especially the rigging components causing or adding to the fatigue (eventual failure) of the rigging/mast 'system
'. This 'harm' would be by the creation of instantaneous 'strength' events that exceed the 'yield strength' of the metals or more commonly events that exceed whats known as the 'fatigue endurance limit'. With fatigue, all these events 'add up' over time and with stainless steels the component will usually catastrophically fail at 1 million load cycles that occur beyond or exceed the fatigue endurance limit
... about 1/3rd the ultimate tensile strength for 300 series stainless (or about 30,000 psi).
• The hands down BEST way to avoid 'mast pumping' is to PRE-BEND or PRE-BOW the mast - changes the natural frequency of the mast.
• The hands down BEST way to reduce mast pumping when sailing
(heavy wind conditions) is to change the tension in the rigging (up or down) ..... until the pumping stops. For 'distance' sailors this is usually accomplished by applying/changing rig/mast tension by the running backstays ... OR at a minimum by changing the backstay tension .... or in extreme mast pumping situations to reduce/increase sail area ... OR sailing direction.
Mast pumping is a potential failure mode of the rigging/mast system.
Most folks simply never add prebow to their masts ... and without pre-bow/pre-bend the pumping can become 'exceptionally violent' under the convergence of the 'right' conditions.
Here's an equivalent of this 'vortices shedding' phenomenon, can happen with sailboat masts, too: https://www.youtube.com/watch?v=nFzu6CNtqec
hope this helps.