Important note, for full credit your deflection and slope equations should be given in terms of the following variables, including the variables shown in this free body diagram where Ro and Rc are the bearing reaction forces and FA and Fa are the forces applied to the shaft at pulleys A and B. Note the points labeled as O, B, C, and A. The distance from O to B; for example, is OB and the distance from O to C is OC. Please label distances in your solution in this way when using the superposition method. a. Using singularity functions, solve for the slope and deflection equations valid for the entire shaft using a single equation in terms of singularity functions and the variables noted above. Ro Free Body Diagram F B C Re A FA b. Simplify the expressions from part (a) to derive equations free of singularity functions for slope and deflection from point O to point B (call the deflection you). Write equations for the slope and deflection in terms of x and the variables noted above. c. Simplify the expressions from part (a) to derive equations free of singularity functions for slope and deflection from point B to point C (call the deflection yc). Write equations for the slope and deflection in terms of x and the variables noted above. d. Simplify the expressions from part (a) to derive equations free of singularity functions for slope and deflection from point C to point A (call the deflection yCA). Write equations for the slope and deflection in terms of x and the variables noted above. e. Plot your deflection and slope solutions for the entire shaft. You must plot your results using Matlab. You can use the example m-file for plotting that was provided on eLearning. Include both the plots and m-file in your submitted solution. Your m-file should include your name. f. Discuss the critical points in the deflection and slope analysis. At what values of x is the deflection or slope zero? What are the maximum slopes and deflections and where do they occur along the shaft? g. With the above solution, you can use your plotting script to evaluate different designs for the shaft. For example, you may be interested to know the slope and deflections for a larger dimeter shaft. Repeat part (f) for an increased shaft diameter of 40mm (0.040m). Plot the deflection and slope for the entire shaft.