Consider a simply supported stepped steel shaft carrying two gears weighing 50 and 75 lbs. as depicted in the figure. Use the method of sections, Castigliano’s Theorem, and Rayleigh’s method to calculate the first critical speed of the shaft. The diameters of shafts BD and DE are 1.5 and 1.75 in., respectively. Gear 1 is located at x=4.5 in, whereas gear 2 is located at x= 14 in. The modulus of elasticity psi(E=30x10^6psi)
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