Question 4: Following is a simplified form of the fuel-pump loop used in helicopters. Consider the long pipe a series connection of II and CLP. Motor V Compliant Shaft q Pump Short Pipe Accumulator Valve Nozzle Long Pipe, I1, CLP (a) Carefully specify the ideal elements that can be used for different parts of the system. You may assume that the relationships for the motor and the pump are: (T and Pd are ideal torque and pressure, respectively) Motor: TK and w= -v Km 1 Pump: q=K, and Pid = -T K (b) Now add the motor friction RM and the pump friction Rp to the ideal elements in Part (a). Draw a bond graph for this system and specify the state variables. (c) Assuming that the flow through the nozzle is the output variable, obtain a set of state equations and an output equation.