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The second Stokes problem about behaviour of the rarefied gas fillinghalf-space is formulated. A plane, limiting half-space, makes harmoniousoscillations in the plane. The kinetic equation with model integral ofcollisions in the form $ \tau $ - model is used. The case of diffusivereflection of molecules of gas from a wall is considered. There are eigensolutions (continuous modes) the initial kinetic equation, corresponding to thecontinuous spectrum. Properties of dispersion function are studied. Thediscrete spectrum of this problem consisting of zeroes of dispersion functionin complex plane is investigated. It is shown, that number of zero ofdispersion function to equally doubled index of coefficient of the problem. Theproblem coefficient is understood as the relation of boundary values ofdispersion function from above and from below on the real axis. Further thereare eigen solutions (discrete modes) the initial kinetic equation,corresponding to the discrete spectrum.  The general solution of the kinetic equation in the form of expansion byeigen solutions with the unknown coefficients corresponding to discrete andcontinuous spectra is worked out. In the present work the analytical solutionof second Stokes problem is constructed. On the basis of the analyticalsolution velocity of gas in half-space is calculated. Also velocity of gasdirectly at oscillating boundary is calculated precisely. The force of afriction operating from gas on the oscillating plate is found, and alsodissipation of energy of a plate is obtained.

Analytical Solution of Second Stokes Problem on Behavior of Gas over Oscillation Surface. Part III: Solving of Problem and Applications