Intrinsic critical speed of a steel circular shaft

[Mechatroni]

Homework Statement

Determine the intrinsic first critical speed of a circular steel shaft supported by two bearings
E=207GPa

How can i determine it I'm very confused about this question , you can see the question at the attachment. Thanks for the help

 

[SteamKing]

Specifically, what are you confused about? Do you understand how to calculate the critical speed of a shaft? Have you been exposed to the Rayleigh Method? Dunkerley's equation?

 

[Mechatroni]

i'm not so good at this lecture. The part I'm confused is there is 3 different regions in the shaft so do i have to calculate for each of them and take the lowest one? i know the Rayleigh Method and the Dunkerley's Equation but i need to use m ( mass ) in those equations , the problem is only E is given to me. Where do i have to start to solve this

 

[SteamKing]

The OP says it is a steel shaft, so you can look up the density of steel and figure the mass of the shaft.

I think your first order of business is to analyze the shaft statically and determine its deflection between the bearings.