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Section 3.7 Free Mechanical Vibrations: Problem 7 Previous Problem Problem List Next Problem (1 point) A mass weighing 2 1b stretches a spring 24 in. Suppose the mass is displaced an additional 12 in in the positive (downward) direction and then released with an initial upward velocity of 2 ft/s. The mass is in a medium, that exerts a viscuouse resistance of 5 1b when the mass has a velocity of 16 ft/s. Assume g = 32 ft/s is the gravitational acceleration. (a) Find the mass m ( in 1b . s2/ft). m = (b) Find the damping coefficient c (in 1b . s/ft). C (c) Find the spring contant k (in 1b/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) = fu/s (f) Is this system under damped, over damped, or critically damped?|