The first step in a damped system is to determine if it is underdamped, overdamped or critically damped. From the given parameters, the natural frequency and critical damping constants are

Since the system damping coefficient (c = 100 N s/m) is lower than the critical damping coefficient (c_c = 220.5 N-s/m), the system is underdamped. The damping ratio is

      ζ = c/c_c = 100/220.5 = 0.4535 < 1 (underdamped)

For an underdamped system, the equation of motion is

The initial conditions now need to be determined. The static deflection δ is

     δ = mg/k = 0.233 m

Taking this as the datum line, the initial conditions are

     y(0) = δ      

     dy(0)/dt = -v

Using the initial conditions, the constants C and D can be calculated as

Substituting the known values give

   y(t) = e^-2.94t (-2.13 sin(5.78t) + 0.233 cos(5.78t)) m

The motion of the container and its acceleration are shown to the right: