$-$ Installed force: $50$ lb $,$ Installed length: $\backslash (2\mathrm{.}15^\{\backslash$prime $\backslash$prime$\}\backslash ),$

$-$ Operating force: $120$ lb $,$ Operating length$/$height: $\backslash (1\mathrm{.}65^\{\backslash$prime $\backslash$prime$\}\backslash )$

$-$ If no suitable standard wire can be found in the textbook, the stress of steel spring wire should not exceed $280$ ksi $.$

Design the following components based on $\backslash (\backslash$mathrm$\{$N$\}=2\backslash ).$

$1.$ Spring $-$ Determine the geometry $($dimensions$,$ number of coils, end condition, length, etc.$)$ of the spring, select$/$specify spring material. Evaluate if the spring would buckle.

$2.$ Rocker arm $-$ The maximum and minimum forces acting on the rocker arm is calculated from the spring. The rocker arm can be considered as a beam $($with a simplified cross section such as a tube or a U$-$channel$).$

$3.$ Push rod $-$ Determine the length and the cross$-$section of the push rod, select the material. Note that the push rod is subjected to cyclic loading. Also the push rod should not buckle $($column loading$).$

$($b$)$ Valve opent: ipring length, $\backslash ($ L$\_\{$Q$\}\backslash )$