A moment $\backslash ($ M$\_\{$o$\}\backslash )$ that varies between $\backslash (\backslash$mathrm$\{$M$\}/2\backslash )$ and M is applied at the end of a cantilever beam as shown below. The cross section of the beam has dimensions $5$ by $5$ mm with an ultimate tensile strength of $770$ MPa $.$ Determine the maximum allowable moment M for which the beam will have an infinite life with a factor of safety of $\backslash (\backslash$mathrm$\{$n$\}=3\backslash ).$ Use Modified Goodman criterion.