Problem

As a result of firing a projectile, a 300 kg naval gun assembly gains momentum in the x di...

As a result of firing a projectile, a 300 kg naval gun assembly gains momentum in the x direction. We can consider the motion of the assembly to start from the equilibrium position x(0) = 0 with an initial velocity ẋ(0) = 50 m/s. Choose values of spring stiffness k and damping coefficient c to provide the fastest return of the assembly to its equilibrium position without oscillation. In addition, make sure that the maximum displacement of the assembly does not exceed 0.1 m. Finally, estimate the time it takes for the gun assembly to return to within 1% of its maximum displacement.