Prob. $4(2$ points$)$

By the Dunkerley method, the weight element W$1$ and the critical speed $($or natural frequency$)n$ of the axis according to the displacement word are expressed by the following equation.

$n_1=\frac{1}{2}\sqrt[\phantom{2}]{\frac{g}{{}_1}}$

If the stiffness coefficient of this system is $k$ and the mass is $m,$ derive $n_1=\frac{1}{2}\sqrt[\phantom{2}]{\frac{k}{m}}$