A 4 [kg] of mass is hung upon the lower end of a coil spring hanging vertically from a fixed support. The mass comes to rest in its equilibrium position, thereby stretching the spring 0.8 [m]. The weight is then pulled down a certain distance below this equilibrium position and released at t = 0. The medium offers a resistance equal to a(dx/dt), where a > 0 and dx/dt is the instantaneous velocity in [m/s]. (a) Determine the displacement of the weight as a function of the time (in terms of a) (b) Determine the value of a such that the motion is in i) damped oscillatory, ii) critically damped, iii) overdamped.

A 4 [kg] of mass is hung upon the lower end of a coil spring hanging vertically from a fixed support. The mass comes to rest in its equilibrium position, thereby stretching the spring 0.8 [m]. The weight is then pulled down a certain distance below this equilibrium position and released at t = 0. The medium offers a resistance equal to a(dx/dt), where a > 0 and dx/dt is the instantaneous velocity in [m/s]. (a) Determine the displacement of the weight as a function of the time (in terms of a) (b) Determine the value of a such that the motion is in i) damped oscillatory, ii) critically damped, iii) overdamped.