A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4

Question

A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4-pound weight is attached. How far does the spring stretch? The mass-spring system of the previous problem is set in motion in a medium that imparts a damping force numerically equal to 2 times the velocity. The mass is pushed up three inches from the equilibrium position and given a downward velocity of 2 feet per second. Write down the initial value problem for the position, x(t), as a function of time. Solve the initial value problem from the previous problem.

Explanation / Answer

restoring force acting on the spring is

            F = kx

           m g = kx

             x = mg / k

                 = 4 pounds / ( 12 pounds/foot )

                 =0.33 foot.

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