$(1)$ Consider a loaded statically determinate beam, as shown in Figure $1.$ Determine the relative displacement between the right and left edges of point $E({}_{E^{-}-E^{**}})$ using $($a$)$ the unit load method, and $($b$)$ the conjugate beam method.

$k_{\frac{L}{2}}**\frac{L}{2}**\frac{L}{2}**\frac{L}{2}**$

Figure $1$