A steel shaft is simply supported by two rolling element bearings at A and C. The length of the shaft is 0.6 m, and two flywheels are attached to the shaft at the locations B and D as shown.

The flywheel at location B weighs 200 N, and the flywheel at location D weighs 90 N. The weight of the shaft can be neglected. It was determined that with flywheel 1 alone, the first critical speed of the shaft is 800 rad/s, and with flywheel 2 alone, the first critical speed of the shaft is 1 200 rad/s.

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

(b) If the two flywheels are interchanged (that is, flywheel 2 is placed at location B and flywheel 1 is placed at location D), determine the first critical speed of the new system using the Dunkerley approximation.

Figure P13.27 Steel shaft simply supported by two rolling element bearings.