For the simply supported beam $(l=20ft)$ subjected to uniformly distributed load $w=10l\frac{b}{f}t.E$ and I are constant. Deformation due to shear is ignored. To find the displacement ${}_m$ at the midspan, please do the following:

$(1)$ please explain all the symbols in the equation below:

$(2)$ According to your explanation in $(1),$ find the function of $m$ with respect to $x$

$(3)$ According to your explanation in $(1),$ find the function of $M$ with respect to $x$

$(4)$ Use the virtual work principle, find the displacement ${}_m$ at the mid$-$span.