Analysis of Longitudinal Motions of Trains by the Electrical Analog

The relative motion of a train of n uniform cars and a locomotive is considered. If slack and rolling resistance are neglected, the system may be idealized to that of (n+1) masses connected by springs. To generalize the analysis it is assumed that identical shock absorbers of the dash-pot or viscous friction type are placed between the units. By considering the electrical analog of this dynamical system, its natural frequencies are determined. It is found that if the shock absorbers have a certain critical strength, no free oscillatory motion between the cars is possible. Expressions are obtained for the velocities of the several cars when the locomotive exerts an oscillatory tractive effort. By the use of the operational calculus, the response of the system when the tractive effort is impulsive is also determined.