Three identical flywheels, each weighing 19 lb, are rigidly attached to a rotating shaft.

The known influence coefficients of the shaft are: a11 = 2.25 × 10−4 in/lb, a22 = 10.75 ×

10−4 in/lb, a33 = 6.25×10−4 in/lb, a12 = 0.80×

10−4 in/lb, a13 = 0.15 × 10−4 in/lb, and a23 =

1.0 × 10−4 in/lb. Use the Rayleigh-Ritz method to determine the first critical speed of the shaft.