A mass weighing 14 pounds stretches a spring 2 feet.
The mass is attached to a dashpot device that offers a damping
force numerically equal
to *β* (*β* > 0) times the
instantaneous velocity. Determine the values of the damping
constant *β* so that the subsequent motion is
overdamped, critically damped, and underdamped.

(If an answer is an interval, use interval notation.
Use * g* = 32 ft/s

(a) overdamped

(b) critically damped

(c) underdamped

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Using the newton second lawk is the spring constanteb positive damping constantm mass attachedm(d^(2)x)/(dt^(2))=-kx-b(dx)/(dt)x(t) is the displacement from the equilibrium position(d^(2)x)/(dt^(2))+(b)/(m)(dx)/(dt)+(k)/(m)x=0Converting units of weights in units of mass (equation of motion)m=(W)/(g)=(14)/(32)=0.43" slug "From hook's law we can calculate the spring constant kk=(W)/(s)=(14)/(2)=7lb//ftIf we put m and k into the DE, we get (d^(2)x)/(dt^(2))+(b)/( 0.43 ... See the full answer