  We have studied the dynamics of a particle in a periodically driven
underdamped periodic potential. Recent studies have reported the occurrence of
Stochastic Resonance (SR) in such systems in the high frequency regime, using
input energy per period of external drive as a quantifier. The particle
trajectories in these systems can be in two dynamical states characterised by
their definite energy and phase relation with the external drive. SR is due to
the noise assisted transition of the particles between these two states. We
study the role of damping on the occurrence of SR. We show that a driven
underdamped periodic system exhibits SR only if the damping is below a
particular limit. To explain this we study the syatem in the deterministic
regime. The existence of the two dynamical states in the deterministic regime
is dependent on the amount of damping and the amplitude od external drive. We
also study the input energy distributions and phase difference of the response
amplitude with the external drive as afunction of the friction parameter.
