Question

The static deflection of a shaft under a flywheel is 4 mm. take g=10m/s2.what is the critical speed in rad/s?

Answer 1

We would calculate the critical speed using The Rayleigh–Ritz method. I would assume the shaft has only one segment.
So W_i = √ g/(y_max)
 where g is the acceleration of gravity, and the w_i is the weights of each segment, and where y_max = 4mm = 4 * 10^(-3)

 So W_i = √ (9.8/0.004)
 W_i = √ 2450 W_i
= 49.49 rad/s