Problem $12\mathrm{.}29.$ Consider the beam shown in $($Figure $1).$ EI

is constant. PART A$.$ Determine the equations of the elastic curve using the x$1$

and x$2$ coordinates.

Express your answers separated by a comma in terms of some or all of the variables x$1,$ x$2,$ a$,$ w$,$ E$,$ I, and L $.$v$1($x$1)$

$,$ v$2($x$2)=?$

$=$ PART B$.$ Determine the slope of the beam at B$,$ measured counterclockwise from the positive x axis.

Express your answer in terms of some or all of the variables a$,$ w$,$ E$,$ I, and L$.$ PART C$.$ Determine the displacement of the beam at B$.$ Express your answer in terms of some or all of the variables a$,$ w$,$E$,$ I, and L$.$ Enter positive value if the displacement is upward and negative value if the displacement is downward.