For the translational mechanical system with a nonlinear spring shown in Figure P2.35, find the transfer function, G(s) = X(s)/F(s), for small excursions around f (t) = 1. The spring is defined by x_s(t) = 1 - e^-fs(t), where x_s(t) is the spring displacement and fs(t) is the spring force.

Nonlinear x(1) spring 2 kg 2N-s/m FIGURE P2.35