1. Bay 1999, Problem 1.4. For the mechanical system in Figure | with a spring, friction forces, and an external force, write state equations using the following sets of variables. Assume that the spring is linear, and that there are linear viscous friction forces on the two masses with damping coefficients B,; and Bz. The input is the force F on the mass m1}. (a) State variable ; =x), 6 = 2%), 63 = x2, and 4 = Xp; and output variable y = x. (b) State variable ; =x), 62 =x), 63 =x2 x), and 4 = x2 X,; and output variable y = x2 x1. Figure 1: Problem | mechanical system