Determination of amplitudes at oscillation of carriages on brake position of moderator-coolant?

We present equations to describe in analytical form a dynamics of a freight carriages group on a sorting hill. The purpose is to determine analytically the amplitudes of oscillations, induced by a braking process on a moderatorcoolant. The groups of carriages needed to be braked may consist of four, six and ten carriages. The theoretically varied parameters are the longitudinal speed of the group and a period of brake apply, as well as types of the freight carriages. The results allow to choose the regime of safe braking in order to avoid the derailment.