Motivated by non-relativistic models of a QCD string, we examine the system
of a non-relativistic string in uniform rotational motion with one end
fixed and with a mass (quark) attached to the other end.  A QCD string has
no purely longitudinal modes so some constraint must be imposed upon the
non-relativistic system to exclude these modes.  Accordingly, we examine
the cases that the string is either inextensible or purely transverse.  For
each case we solve first the discretized string and then do the continuum
case.  We find the small amplitude oscillatory motions and frequencies of
oscillation of the string and mass.  We show that the assumption of a node
at the end of the inextensible string produces frequencies that are very
close to the actual frequencies.  For the transverse string, we show that
keeping centrifugal terms for the motion of the masses comprising the
string leads to an unstable mode.