The shaft is simply supported by the bearings at A and D. Flywheel 1 at location B weighs 5.6 lb, flywheel 2 at location C weighs 17.9 lb, and the weight of the shaft can be neglected. The influence coefficients of the shaft are a11 = 1.8×

10−8 in/lb, a12 = 0.7 × 10−8 in/lb, and a22 =

9.8×10−8 in/lb. Determine the first critical speed of the shaft using:

(a) the Dunkerley approximation, and

(b) the Rayleigh-Ritz approximation.