Yaw dampers are fitted to damp dutch roll oscillations which may be greater than that permitted by the certification standard.
If by "coordinated" you mean zero sideslip, then that is the job of the fin.
As John Farley wrote, the spiral mode is weak and may be either positive or negative. It may change sign with configuration or altitude.
A simple way to look at the spiral mode would be if directional stability is dominant, then the sideslip resulting from bank would cause the aircraft to "weathercock" into wind, the outside wing lift increases and the bank angle further increases - spiral dive.
If lateral static stabilty (dihederal effect) dominates then the sideslip caused by bank results in a roll away from the direction of sideslip, reducing the bank angle.
It is a fine tuning job to achieve the required levels of static and oscillatory stability, often poor oscillatory stability is the result and this is fixed with a yaw damper.
Irrespective of entering a coordinated turn, one has to release the controls to view the behavior under the forces resulting from the various stabilities
Last edited by zzuf; 13th March 2014 at 05:30.
Reason: clarify post