$7-35$ Compare ubrace$(\frac{?}{{?}_{\frac{?}{?}}\text{u}\text{b}\text{r}\text{a}\text{c}\text{e}})$ Equation $(7-27)$ for the angular frequency of a two$-$disk shaft with Equation $(7-28),$ and note that the constants in the two equations are equal.

$($a$)$ Develop an expression for the second critical speed.

$($b$)$ Estimate the second critical speed of the shaft addressed in $$ Example $7-5,$ parts a and $b.$