I think I understand your problem, you are obviously struggling hard with our wierd language.
The best way to look at the problem, if I understand correctly, is that you are seeing changes in fluid velocity. Each time the velocity changes rapidly, the pipe "dances".
Now, if that be true then you are looking for anything that would change the velocity rapidly. Some items, based on my casual experience are:
INTAKE CONSIDERATIONS:
1 - Air or other gasses entering the pump, from leaks in the intake line, from the end of the suction picking up air from a vortex or swirl, or from depressurization of the liquid as it travels through the intake line if the liquid is super saturated or highly saturated with gasses that can come out of solution due to the drop in liquid pressure inside the intake line or pump internally.
2 - It is possible that the pump or it's intake structure and supply is improperly applied or selected, resulting in internal pump misbehavior such as cavitation. However those things DO not usually affect the discharge pipe systems violently unless very extreme. I will not go into this area at this time unless I know that you can understand and do calculations for NPSHr vs. NPSHa, etc.
DISCHARGE ITEMS
1 - Rapid velocity changes due to rapidly closing or opening valves, especially relief valves, fast manual closure of ball or butterfly valves, malfunctioning control valves, chattering valves.
2 - If an accumulator or pressure tank is present then that item may have problems such as incorrect settings, no air pre-charge (water logged), etc. There must usually be some form of energy storage or static head on a discharge line to prevent rapid changes in pressure.
PUMPDESIGNER