a) A hydraulic servomechanism with mechanical feedback is shown in Fig. Qla. The input to the system is the lever movement x while the output is the piston displacement y. The power piston has an area equal to A. When the valve is moved a small amount x,, the oil will flow through to the cylinder at a rate of q. The input pressure of oil is assumed to be constant. The mathematical model of the system is described by the following three equations: (1) x, () == 2 x (x()-y())- y0) 4 9 (1)=Cx (1) 9 (1)=Ady (1) dt (2) (3) where k is a constant and C, is the port coefficient. 1. Obtain the Laplace transform of the mathematical model (the above three equations), assuming zero initial conditions. 2. Determine the block diagram for the system. Input pressure k(x-y) Input, x Power cylinder Output, y (3 marks) (3 marks)