A shaft is simply supported at A and B and is rotating with constant angular velocity ω. Two identical flywheels C and D of unknown mass are rigidly attached to the shaft (at locations 1 and 2). The known influence coefficients are a11 = 41.1 × 10−6 in/lb, a12 = 29.4 × 10−6 in/lb, and a22 = 53.3 × 10−6 in/lb. The first critical speed of the shaft, obtained from the exact equation, is 135 rad/s. Determine:

(a) the masses of the two flywheels, and

(b) the second critical speed of the shaft.