Amass weighing 10lb stretches a spring 30in. suppose the mass is displaced an additional 2in 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 5lb when the mass has a velocity of 16ft/s assume g=32ft/s2 is the gravitational acceleration.
(a) find the mass m ( in lb⋅s2/ft).
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 xx 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?