A steel shaft, which is 50 inches in length, is simply supported by two bearings at B and D. Flywheels 1 and 2 are attached to the shaft at A and C, respectively. The flywheel at location A weighs 15 lbs, the flywheel at location C weighs 30 lbs, and the weight of the shaft can be neglected. The stiffness coefficients are specified as k11 = 2.5 ×

104 lb/in and k22 = 4.0×104 lb/in.

(a) Determine the first critical speed for the two-mass system using the Dunkerley approximation.

(b) If the two flywheels are interchanged (that is, flywheel 2 is placed at location A and flywheel 1 is placed at location C), determine the first critical speed of the new system.