external force P acts on point A and B $.$ For case $($b$),$ distributed load p $($unit: N$/$m$)$ is applied between points C and D $.($To convert to force, multiply $\backslash ($ p $\backslash )$ and length$)$ For case $($c$),$ external force $2$ P acts on point E and external force P acts on point F $.$ The diameter of each rod is as shown in the figure. The Young's Modulus of each rod is E$.$ Please solve the following problems.

$($a$)$

$($b$)$

$($c$)$

Fig. $1$

$(1)$ For each case, determine the reaction force from the wall, $\backslash ($ R a$,$ R b$,$ R c $\backslash ),$ and draw the FBD $($Free Body Diagram$).$

$(2)$ For each case, draw the variation of the axial force in the x $-$direction, $\backslash ($ N$($x$)\backslash ),$ in a graph with $\backslash ($ x $\backslash )$ on the horizontal axis and $\backslash ($ N $\backslash )$ on the vertical axis.

$(3)$ For each case, draw the variation of the axial stress in the x $-$direction, $\backslash (\backslash$sigma$($x$)\backslash ).$

$(4)$ For each case, determine the displacement $\backslash (\backslash$delta $\backslash )$ at $\backslash ($ x$=$L $\backslash ).$