The first critical speeds of a rotating shaft with two mass disks, obtained from three different mathematical techniques, are 150 rad/s, 152 rad/s, and 153 rad/s, respectively. The influence coefficients a11 = a22 = 3 × 10−4 m/N.

(a) Specify which value corresponds to the first critical speed from the exact solution, the Rayleigh-Ritz method, and the Dunkerley approximation.

(b) If the masses of the two disks are identical, then use the Dunkerley approximation to calculate the mass of each disk.

(c) If the masses of the two disks are specified as m1 = m2 = 0.10 kg, then use the Rayleigh-Ritz method to calculate the influence coefficient a12.