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A machine tool spindle is supported by two rolling contact bearings as shown if figure below. The front bearing has a stiffness Si of 1000 N/um, and the rear bearing has a stiffness S2 of 600 N/um, the overhang a is 100 mm and the spindle diameter d is 75 mm. The modulus of elasticity E of the spindle material is 210 x 10' N/mm². The distance between the bearings is b with a correlation a = a/b. The deflection per unit load f is given by: a? 1 1 a)2 + 2a ЗЕІ na" 64 where I = is the moment of inertia of the spindle section. Determine the spindle spacing b for minimum deflection per unit load (i.e., maximum stiffness). [Ref: Belegundu & Chandrupatia, 3rd Ed., 20191 S Deflected center line S 17 - First formulate the problem, and then solve: 1. Analytically. 2. By hand, using the Golden Section Method for the first 10 function evaluations (and not 10 iterations). 3. Numerically, using the Golden Section algorithm, you will code and hand-in via D2L. 4. Compare the results obtained in 1, 2, 3 in table form. Finally, comment on the output in a separate column.