A slight vertical bobbing movement of the tail is low frequency vibration, hence it is coming from the main rotor system. There are several ways to check and correct this.

1. Insure the main rotor shaft is straight and running true. You may be surprised how many shafts are not straight.

2. Make sure the main rotor blade grips are tightened equally. Both blades must be free to lead/lag, though snug, with equal tension. If applying only more head speed solves the shake, then this is your problem.

3. Static balance of M/R blades may be accurate but dynamic balance may be off (that is why tire shops spin balance tires). A simple test is to tightly snap a #44 or so rubber band around the center (chordwise) of one blade. Lift off and if there is improvement, start moving the band inward or out and note difference. If not, move it to the other blade. If nothing improves using this method, the blade balance is okay. If moving the band smoothes out the shake, begin adding strips of sticky blade covering (vinyl, monokote, etc.) the bands location after removing it. Add more to achieve balance.

4. Be sure the flybar is straight, any bend causing lead or lag will contribute to the shake. Remove the flybar paddles and add several wheel collars to each side, moving them close to the hub. Start sliding one collar out about half way and lift off. If improvement, continue making fine adjustments to that side. If none, go to the other side. If no improvement on either, the flybar is dynamically balanced.

Years ago, blade balancing accuracy was performed by first finding the individual blade's center of gravity length wise and adding little pieces of covering to match the blades. Then they were covered and balanced as a unit on a balancer or on the rotor head (less accurate). Today's precovered/balanced(?) blades are matched by weight only, however their CG mass may not be in identical locations.

Try these steps. There is no reason to fly any heli with a shake. It will eventually lead to a mechanical failure.