Figure shows $75$ mm diameter solid shaft that is to be designed for minor shock loading. It is desired that the shaft be machined using unnotched steel and that the torque could fluctuate $\backslash$pm $5\%$ about a mean value. Assuming a suitable material for the shaft, compute the factors of safety, n for the following:

$($a$)$ Using DE$-$Goodman criterion

$($b$)$ Assuming a $90\%$ survival rate and using DE$-$Soderberg criterion

$($c$)$ Assume Kf and Kfs $=1\mathrm{.}5($minor shock$)$