Consider the translational mechanical system with a nonlinear spring shown below. The spring is defined by s(t)=ks(t), where x(t) is the spring length and f(t) the spring force. Nonlinear spring 0000 x(t) 2 kg f(t) 2 N-s/m a) Find the non-linear differential equation characterizing the motion x(t) of the mass. b) Linearize the previous equation for small excursions of about f(t)=1 N. c) Find the linear transfer function, G(s) : = X(s) F(s)