The 72-in-long shaft is simply supported by the bearings at B and D. Flywheel 1 at location A weighs 9 lb, and flywheel 2 at location C weighs 16 lb. The weight of the shaft can be neglected. The stiffness coefficients of the shaft are k11 = 5.6 × 103 lb in, k12 = 33.6 × 103 lb/in, and k22 = 22.4 × 103 lb/in. Determine the first and second critical speeds of the shaft using the exact equation. Then, determine the first critical speed of the shaft using:

(a) the Rayleigh-Ritz method, and

(b) the Dunkerley approximation.