On the motion of a system with a moving internal element in the presence of external viscous friction

We consider a system consisting of a translationally moving platform along a fixed line with viscous friction and a body committing a given translational motion relatively to the platform due to internal forces along the same line. In relative motion the value of the body velocity is limited. It is proved that, in the case of linear viscous friction, the unlimited displacement of the platform in any direction is impossible. In the general case under certain conditions imposed on the force of viscous friction, the velocity of the platform is limited. At the same time, if the displacement of the platform in any direction, for example to the right, is unlimited, then with the growth of time the value of the platform velocity changes its sign infinite number of times, and the total time of platform motion to the left and the path passed at the same time tend to infinity.