$3.\backslash ((50\backslash \%)\backslash )$ Consider a cantilever beam with constant $\backslash ($ E I $\backslash )$ and an additional spring support at the free end, as shown in Figure $3.$ Neglect shear effect.

$($a$)$ Analyze statical determinacy of the structure.

$($b$)$ Find the force in the spring.

Now consider that the spring is replaced by a roller support at $\backslash ($ B $\backslash ).$

$($c$)$ Find the reaction force at $\backslash ($ B $\backslash ).$

$($d$)$ Find the deflection and rotation at the midpoint of the beam.

Figure $3$