Control Systems - Unit Impulse Simple Question?

It is not an impulse, it is a constraining force that has done work on compressing the damper through some (unindicated) distance.I would treat this as a compressed spring, with potential energy of Force * Distance_of_compression, and when the constraining force is released treat the result as an oscillating mass with a damping coefficient. i.e., upon freely allowed to move, the initial decompression force might well be 5.0 kN, and that would go to zero at equilibrium position after moving through some damping force for the offset distance, at which time the resultant energy would be kinetic, and so it goes. hth.