A perturber may excite a coherent mode in a star cluster or galaxy .
If the stellar system is stable , it is commonly assumed that such a mode will be strongly damped and therefore of little practical consequence other than redistributing momentum and energy deposited by the perturber .
This paper demonstrates that this assumption is false ; weakly damped modes exist and may persist long enough to have observable consequences .

To do this , a method for investigating the dispersion relation for spherical stellar systems and for locating weakly damped modes in particular is developed and applied to King models of varying concentration .
This leads to the following remarkable result : King models exhibit very weakly damped m = 1 modes over a wide range of concentration ( 0.67 \leq c \leq 1.5 have been examined ) .
The predicted damping time is tens to hundreds of crossing times .
This mode causes the peak density to shift from and slowly revolve about the initial center .
The existence of the mode is supported by n-body simulation .

Higher order modes and possible astronomical consequences are discussed .
Weakly damped modes , for example , may provide a natural explanation for observed discrepancies between density and kinematic centers in galaxies , the location of velocity cusps due to massive black holes , and m = 1 disturbances of disks embedded in massive halos .
Gravitational shocking may excite the m = 1 mode in globular clusters , which could modify their subsequent evolution and displace the positions of exotic remnants .