The spring in the mass$-$spring model can be replaced by an elastic body, such as the vertical rod as shown in Fig. $1.$ Calculate maximum deflection of the rod, assuming: $m=1kg,L=2m,h=1m,$ Cross$-$sectional area of the rod, $A=0\mathrm{.}0001m^2.$ Use $E=200$ GPa and $g=9\mathrm{.}8\frac{m}{s^2}.$

Figure. $1$: A vertical rod an example of elastic body.

${}_{\text{m}\text{a}\text{x}}=n{}_s=\sqrt[\phantom{2}]{\frac{2h}{{}_s}}{}_s=\sqrt[\phantom{2}]{2h{}_s}=\sqrt[\phantom{2}]{\frac{2hL}{EA}mg}$