A helical compression spring is wound using $3\mathrm{.}5-mm-$diameter wire. The spring has an outside

diameter of $50\mathrm{.}6$ mm with squared and ground ends, and $5\mathrm{.}5$ total coils. The suggested free length

of this spring is $75\mathrm{.}5$ mm $.$ The material of this spring is OQ&T wire. Investigate this helical

compression springs to see if it is solid$-$safe considering using factor of safety, $n_s=1\mathrm{.}2.$ If not,

what is the largest free length to which it can be wound using factor of safety, $n_s=1\mathrm{.}2?$

Note that, for OQ&T wire material, torsional yield strength is $50\%$ of ultimate strength i$.$e$.$

$S_{sy}=0\mathrm{.}5S_{ut.}$