Amass weighing 6lb stretches a spring 15in. suppose the mass is displaced an additional 9in in the positive (downward) direction and then released with an initial upward velocity of 4ft/s. the mass is in a medium, that exerts a viscuouse resistance of 1lb when the mass has a velocity of 2ft/s. assume g=32ft/s2 is the gravitational acceleration. (a) find the mass m (in lb middot s^2/ft). m = (b) find the damping coefficient c (in lb middot s/ft). c = (c) find the spring constant k (in lb/ft). k = (d) set up a differential equation that describes this system. let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x". (e) enter the initial conditions: x(0) = ft, x'(0) = ft/s (f) is this system under damped, over damped, or critically damped?