  We consider a point mass on a horizontal plane. The motion of the plane is
given. The plane moves periodically such that all its points have congruent
closed trajectories. There is the Coulomb friction between the point mass and
the plane. We show that there exists a motion of the point mass such that the
velocity of the point mass is an absolutely continuous periodic function.
Mathematically the result is expressed as an existence theorem for a periodic
solution to some differential inclusion.
