The mass m = 4 slug and the spring constant is k = 72 lb/ft. The spring is unstretched whe...

The mass m = 4 slug and the spring constant is k = 72 lb/ft. The spring is unstretched when ,x = 0.

(a) What value of the damping constant c causes the system to be critically damped?

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(b) Suppose that c has the value determined in part (a). At t = 0, x = l ft and dx/dt= 4 ft/s. What is the value of.x at t = 1 s?