  The second Stokes problem about behaviour of the rarefied gas filling
half-space is formulated. A plane, limiting half-space, makes harmonious
oscillations in the plane. The kinetic equation with modelling integral of
collisions in the form tau-model is used. The case of diffusive reflection of
molecules of gas from a wall is considered. There are eigen solutions
(continuous modes) the initial kinetic equation, corresponding to the
continuous spectrum. Properties of dispersion function are studied. The
discrete spectrum of this problem consisting of zeroes of dispersion function
in complex plane is investigated. It is shown, that number of zero of
dispersion function to equally doubled index of coefficient of the problem. The
problem coefficient is understood as the relation of boundary values of
dispersion function from above and from below on the real axis. Further there
are eigen solutions (discrete modes) the initial kinetic equation,
corresponding to the discrete spectrum. The common solution of the kinetic
equation in the form of expansion by eigensolutions with the unknown
coefficients corresponding to discrete and continuous spectra is worked out.
