Shown below is a schematic of a ship's propeller, drive train, engine and flywheel. Flywheel having a very large inertia can be assumed to be fixed. The input torque Tm is applied by the engine. The diameter ratio of gears is D/D=0.5. J and J are the rotational inertias of engine and propeller , respectively. Rotational stiffnesses of shafts 1 and 2 are K and K, respectively. Rotational inertias of gears 1 and 2 are represented by I and I respectively. The nonlinear fluid damping torque on the propeller is a function of angular velocity : TNLD = 50002 + (0). The linear damping torque on the engine is a function of angular velocity : TLD = B Shaft 1 Flywheel Engine D Shaft 2 Propeller The values of the model parameters are: J=1000 kg-m; J2-800 kg-m I=100 kg-m; L=400 kg-m; K=10000 N-m/rad; K=20000 N-m/rad B=600 N-m-sec/rad; B=2200 N-m-sec/rad 1. Develop a nonlinear state space model for this system. Use q0,92 = , 93 = 0 and 94 = 2 as the state variables. The output of the system is the angular displacement of propeller. Also, construct the simulation diagram. 2. Use the MATLAB program ode45 to calculate and plot the output of the system to a step torque(Tm) with magnitude 100 N-m and then to a step torque with magnitude 300 N-m. For both inputs, determine the steady- state value, maximum overshoot, and period of oscillations of the output. Include a print out of your MATLAB program. 3. Linearize the system model in the vicinity of the normal operating point, Tm=0. 4. Obtain step responses of the linearized model for the same two step inputs. Again, for both inputs determine steady-state value, maximum overshoot, and period of oscillations. Compare these values with those from the nonlinear system. Include a print out of your MATLAB program. 5. For the linearized state space model, find the transfer function and input-output differential equation; and make the pole-zero map. For each complex pole, find the damping ratio and undamped natural frequencies. Are there dominant roots? If yes, use dominant roots to estimate maximum overshoot and period of oscillations. 6. Write your conclusions regarding all important aspects of this project. Specifically, is the linearized model a good representation of the nonlinear model? Is the concept of dominant roots valid here? 7. As an engineer you are asked to certify this ship's propeller, drive train, engine and flywheel on the basis of step response and the assumption of a fixed flywheel. What will be your professional decision. (Refer to Ethics in Engineering & Engineering Groups - ASME)