A small turbine has a uniform section El $1\mathrm{.}17{10}^6(N{m}^2).$ It is freely supported in two bearings at a distance of $3$ m in length. It carries three equal discs of $4$ kN at each position $0\mathrm{.}46m,0\mathrm{.}71m$ and $1\mathrm{.}3$ m from bearing A$.$ Ignore the mass of the shaft, and calculate the critical speed of the turbine in revolution per minute units $($RPM$).$