A stepped round steel shaft for which $E=200$GPa is supported by two bearings and carrying

the flywheel weight $W=400N.$ The moment of inertia $(21)$ of the shaft in its central region is twice that of

the moment of inertia $($ I $)$ in the end parts and $L=1m,I=0\mathrm{.}3{10}^{-6}{m}^4.$ Calculate the critical speed in rpm $.$

Note that the weight of the shaft weight is ignored and the bearings act as simple supports.