There are different kinds of shaking that can occur. if it is just the tail, it can be the gyro gain is too high, the tail pushrod linkage or slider is loose, or the engine may be surging (do you see exahust surging when this happens?)

other types of shaking come from bent spindle or mast, RPM tool low, blades out of track or out of ballance...

My TT39 had a bad surging problem, if your engine is surging the fix is to run the idel needle richer or do the idle needle mod (grind the needle so it has a double taper tip that goes to more of a point)