Amass weighing 6 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/s2 for the acceleration due to gravity.) (a) overdamped

Answer with Step-by-step explanation:

Let m be the mass attached and k be the spring constant and be the positive  damping constant.The Newton's second law for the system is given by

Where x(t) is the displacement from the equilibrium position.

The equation can be written as

Weight=W=6 lb

s=2 feet

a.The motion is overdamped when or

b.The motion is crirtically damped when   or

c. The motion is underdamped when   or

step-by-step explanation: