Are you sure that is your drive shaft and not gear backlash from the gears? In the condition you describe you have to understand what is happening and that is a force transfer condition everywhere. Think of it this way: Imagine two simple gears, one powered, one not and they are meshed together. When one is driven, force is applied on one side of the meshed teeth which causes the other gear to rotate. With me so far? Alright, now start to freewheel the driven gear. This will cause less force to be transmitted and an almost "floating" condition between the meshed teeth down near the root. Now I suddenly accelerate the driven gear, that "space" (backlash) is instantly taken up between the meshed teeth and all is well with the world. That instant that the gear resumes acceleration there will be a transfer of forces and in the condition you describe, it will be felt. It happens to me all the time too. Does it do this if you accelerate gently from freewheel?
(disclaimer: I intentionally left out some of the more technical points to illustrate this condition)
Explanation of backlash:
In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. One source defines it as the maximum distance through which one part of something can be moved without moving a connected part. An example, in the context of gears and gear trains, is the amount of clearance between mated gear teeth. It can be seen when the direction of movement is reversed and the slack or lost motion is taken up before the reversal of motion is complete. Another example is in a valve train with mechanical tappets, where a certain range of lash is necessary for the valves to work properly.
Depending on the application, backlash may or may not be desirable. It is unavoidable for nearly all reversing mechanical couplings, although its effects can be negated or compensated for. In many applications, the theoretical ideal would be zero backlash, but in actual practice some backlash must be allowed to prevent jamming. Reasons for the presence of backlash include allowing for lubrication, manufacturing errors, deflection under load, and thermal expansion.