Find the damping ratio and natural frequency for each second-order system of Problem 8 and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem. [Section: 4.5].

Suppose that 27 j of work is needed to stretch a spring from its natural length of 6 m to a length of 9 m. (a) how much work is needed to stretch the spring from 12 m to 14 m? j (b) how far beyond its natural length will a force of 78 n keep the spring stretched?