Consider the pulley system is used to keep blocks W$\_1$ and W$\_2$ in equilibrium, as shown in Figure P$1.$ Block W$\_1$ has a weight of $\{13\}$ kN$.$ The support at point C experiences a load of $\{93\}$ kN$.$

a$)$ Determine the tension force at point S$.$ Provide your answer in kN to at least $4$ decimal places. $[1$ mark$]$

Tension in cable at point S $[$kN$]=$

b$)$ Determine the tension force at point T$.$ Provide your answer in kN to at least $4$ decimal places. $[2$ marks$]$

Tension in cable at point T $[$kN$]=$

c$)$ Determine the tension force at point U$.$ Provide your answer in kN to at least $4$ decimal places. $[2$ marks$]$

Tension in cable at point U $[$kN$]=$

d$)$ Consider the scenario where the hook at support A is replaced by $3$ springs in a parallel configuration. The springs have stiffness k$\_1=\{7\mathrm{.}2\}$ kN$/$m and k$\_2=\{6\mathrm{.}5\}$ kN$/$m$.$ The total extension of the parallel configuration is $\{1\mathrm{.}4\}$ m$.$ Determine the spring stiffness of k$\_3.$ Provide your answer in kN$/$m to at least $4$ decimal places. $[2$ marks$]$

k$\_3$ spring stiffness $[$kN$/$m$]=$