The propagation and damping of long waves produced by atmospheric pres
sure waves in shallow seas, where quadratic bottom friction has to be
taken into account, was studied analytically. Forced circular motion o
f the open sea, in which quadratic friction is without higher harmonic
s, was analyzed and a solution at the fundamental frequency for a narr
ow channel was obtained. Particular attention was paid to the changes
of elevation amplitude and coefficient of linear friction in both case
s along the resonance lines in the OMEGA - K plane. For the open sea f
orced close to the resonance, the elevation amplitude changes from the
inverted barometer response, when the angular frequency is equal to t
he Coriolis frequency f, to an congruent-to 25 times higher response,
when the angular frequency is 3 f. For a narrow channel forced at the
resonance, the response and coefficient of linear bottom friction are
proportional to the square root of the frequency, achieving changes of
one order of magnitude for the angular frequency between zero and the
Coriolis frequency. In both cases, the drag coefficient of the bottom
friction was supposed to be congruent-to 3 x 10(-3) the depth of the
sea 100 m, and the amplitude of the atmospheric wave 10 cm in elevatio
n units.