Math_Physic Question2

A mass m of 39.57 kg is travelling towards the left, on a straight frictionless, horizontal track onto buffers at a constant speed of 0.9 ms-1 when at t = 0, it hits the buffer. The buffers are to be modelled by a model spring, with stiffness 106.5 Nm-1, together with a model damper with damping constant 196.46 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 0.68 m. The equation of motion is given by, where a, b and c are some constants.

 

Refer to the attachment

Question

A mass m of 39.57 kg is travelling towards the left, on a straight frictionless, horizontal track onto buffers at a constant speed of 0.9 ms-1 when at t = 0, it hits the buffer. The buffers are to be modelled by a model spring, with stiffness 106.5 Nm-1, together with a model damper with damping constant 196.46 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 0.68 m.
The equation of motion is given by, where a, b and c are some constants.

where a, b and c are some constants.
When m = 39.57, determine is the value of c? Give your answer to 3 decimal place.
The system of model damper and model spring is shown below.

Answer: