  We consider the free Klein-Gordon equation with periodic damping. We show on
this simple model that if the usual geometric condition holds then the decay of
the energy is uniform with respect to the oscillations of the damping, and in
particular the size of the derivatives do not play any role. We also show that
without geometric condition the polynomial decay of the energy is even slightly
better for a highly oscillating damping. To prove these estimates we provide a
parameter dependent version of well known results of semigroup theory.
