Vibrational modes of a rotating string

Motivated by nonrelativistic models of a QCD (quantum chromodynamic) string , we examine the system of a nonrelativistic string in uniform rotational m otion 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 nonrelativistic system to exclude these modes. Accordingly , we examine the cases that the string is either inextensible or purely tra nsverse. For each case we solve first the discretized string and then do th e continuum case. We find the small amplitude oscillatory motions and frequ encies of oscillation of the string and mass. We show that the assumption o f a node at the end of the inextensible string produces frequencies that ar e 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.