Consider the mechanical system with a nonlinear spring shown in Figure 3. The relationship between the spring force, f(t), and the displacement, x(t), is f(t) = 2x (t). Assume the output to be the displacement of the mass, x(t). Answer the following questions. a. (3 marks) Write the equations of motion in time domain (2nd-order differential equation). b. (2 marks) Find the equilibrium point when the applied force is f = 10 + f(t) where of (t) is a small force about the 10 N constant value. Is this point a natural equilibrium point or an operating point? Explain. c. (5 marks) Determine the linearized form of the system about the equilibrium point either in state space form (by choosing displacement x and velocity as state variables) or in transfer function form (by finding 8X(s)/8F(s)). h Nonlinear spring 0000 H 1 kg Figure 3 x(1) f(t)