Question

A railway buffer consists of a pair of cylinders placed parallel side-by-side. Oil is present in each cylinder and is arranged to bypass through ports, thereby producing a damping resistance, which is proportional to the velocity of the piston within the cylinder. The magnitude of this resistance is 50 kN at a velocity of 0.25 m/s. Each cylinder also contains a compression spring, initially with negligible compression, of stiffness 65 kN/m. A rigid train of mass 250 tons is moving at a speed of 1.6 m/s and collides with the buffer. Determine the distance taken by the train before first coming to rest. Assuming that the train comes into contact and then become attached to the free end of the buffer. Determine the time it takes the train to come to a complete stop. Solution for this problem should show the position and velocity of the train.

Answer 1

Note: The meaning of the third sentence in the problem ('the magnitude of resistance'), has been taken as the magnitude of resistance by each cylinder since the context contains the description of each cylinder.

If the meaning is not as per what has been interpreted in the solution, the resulting system would be underdamped and the solution would come out different. But since it is logical to stop a train without periodic motion, there is more chance of the system being overdamped than underdamped.