A mass m of 49.4 kg is travelling towards the left, on a straight frictionless,

Question

A mass m of 49.4 kg is travelling towards the left, on a straight frictionless, horizontal track onto buffers at a constant speed of 2.46 ms-1 when at t = 0, it hits the buffer. The buffers are to be modelled by a model spring, with stiffness 133.68 Nm-1, together with a model damper with damping constant 203.23 Nsm-1. The x-axis is chosen directed away from the buffers down the track (in the direction opposite to the incoming mass), with origin at the fixed end of the model spring. The natural length of the model spring is 0.56 m. The equation of motion is given by. where a, b and c are some constants md2x / dt2 = adx / dt = bx = c where a, b and c are some constants. When m = 49.4, determine is the value of c? Give your answer to 3 decimal place. The system of model damper and model spring is shown below.

Explanation / Answer

c = ma But it is moving with constant speed of 2.46m/sec =>a = 0 =>c = 0

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