Consider a cylinder rolling on a board: flat board on a fulcrum T cylinder free to roll on board R As shown, the angle of tilt is denoted by 0, the torque applied to the beam is 7, and d measures the distance the cylinder rolls down the board. Let J denote the mass moment of inertia of the beam (about the fulcrum pivot) and Jc, Re and Me the mass moment of inertia, radius and mass of the cylinder, respectively. Assuming roll without slip, the equations of motion can be shown to be Jc + Me) + Mcg sin0 Mcdo = 0 0 (Mc + J + Jc) + 2Mdd + Mcgd cos (a) What is the order of the system, i.e. what is the required dimension of the state vector x? (b) Put the system into the state model form * = f(x, u), y = h(x, u) using 7 as the input and d as the output. = T.