For a (25 mathrm{~mm}) diameter (6061-mathrm{T} 6) aluminum (operatorname{rod}left(ho=2,700 mathrm{~kg} / mathrm{m}^{3} ight.) and (E=70 mathrm{GPa}) )

For a \(25 \mathrm{~mm}\) diameter \(6061-\mathrm{T} 6\) aluminum \(\operatorname{rod}\left(ho=2,700 \mathrm{~kg} / \mathrm{m}^{3}\right.\) and \(E=70 \mathrm{GPa}\) ) with a nominal length of \(190 \mathrm{~mm}\) and an associated uncertainty of \(0.2 \mathrm{~mm}\), determine the uncertainty in the second bending natural frequency, \(u\left(f_{n, 2}\right)\) (in \(\mathrm{Hz}\) ), if free-free boundary conditions are imposed. You may neglect the uncertainty in \(E, ho\), and \(d\).