The problem of damping of the satellite fast-linear oscillations about its center of mass on yaw and roll channels is considered. The satellite is moving along a stationary orbit and equipped with a hard spun flywheel with a kinematic momentum H. The controlled motion of the satellite can be represented by the linear ODE system with constant coefficients. The admissible control is a piecewise constant function that blanks fast frequency components of the solution of linear equations at the moment T. As "the expenditure" functional we use the integral of the sum of the modules of coordinates of the control along the interval [0, T]. The problem under consideration is to construct an admissible control which minimizes the expenditure. To solve this problem the method is proposed which leads to explicit formulas.