A straight prismatic beam $AD$ has a rectangular cross$-$section with width $b$ and height $h,$ and a total length of $3l.$ Its Young's modulus is $E.$ The beam is subjected to two concentrated moments of equal magnitude, $M_1,$ at $B$ and $C,$ as shown in the figure below.

$(1)$ Please use me energy methed to determine the reaction forces and moments at both ends of the beam, i$.$e$.,$ at $x=0$ and $x=34.(20$ pts$)$

$(2)$ Please use the energy method to determine the slope of the deflection curve, $v^{\text{'}},$ at $x$~~$l.$

pts$)$

$(20)$

$(3)$ Please use the energy method to determine the defleotion, $v,$ at $x=26,(20$ pts$)(20$ pts$)$

serermine the slope of the deflection curve, $v^{\text{'}},at,x=\frac{9}{3}\frac{?}{?},$

to determine the whole deflection curve, $v(x),($Monus: $30$ Pts $)$