For the cantilever beam ABC, shown in figure, $E=30{10}^6$ and $I=50i{n}^4,w=2ki\frac{p}{f}t$ and $L=8ft.$ Determine

$($a$)$ deflection curve from $B$ to $C($express your result in terms of the axial coordinate $x)$

$($b$)$ the deflection at $C($express you result in inches$)$

$(45$ pts$)$