A mass weighing 10 lb. ft/s² stretches a spring 30 in. Suppose the mass is displaced an additional
7 in in the positive (downward) direction and then released with an initial upward velocity of 3 ft/s.
The mass is in a medium, that exerts a viscuouse resistance of 1 lb when the mass has a velocity of
16 ft/s. Assume g = 32 ft/s² is the gravitational acceleration.
(a) Find the mass m (in lb).
m =
(b) Find the damping coefficient c (in lb · s/ft).
c=
(c) Find the spring contant k (in lb/ft).
k=
(d) Set up a differential equation that describes this system. Let $x$ to denote the displacement, in feet,
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? ?