We investigate nonlinear springs. A spring is linear if it obeys Hooke’s Law, which indicates that the applied force to stretch the spring is F(x) = kx. For a linear spring, F' is constant. If, instead, F' is not constant, then the spring is called nonlinear. Furthermore, if F' (x) increases as x increases, then the spring is said to be progressive, and if F'(x) decreases as x increases, then the spring is said to be degressive.

(a) Of the two applied force graphs in Figure 6, which describes a progressive spring, and which describes a degressive spring?

(b) For each, approximate the work required to stretch the spring from 4 to 9 cm.

80 60 40 20 2 4 (A) 6 8 10 X 80 60 40 F 20- 2 4 (B) 6 8 + 10 X