$(1)$ 対称性より\[ R_A=R_B=\frac{1}{2}ql \] $(2)$ \[\begin{align} M &=R_Ax-\frac{1}{2}qx^2-M_A\\ &=\frac{1}{2}qlx-\frac{1}{2}qx^2-M_A \end{align}\] $(3)$ \[ EI\theta=\frac{1}{6}qx^3-\frac{1}{4}qlx^2+M_Ax+C_1\\ EI\omega =\frac{1}{24}qx^4-\frac{1}{12}qlx^3+\frac{1}{2}M_Ax^2+C_1x+C_2\] \[ x=0で\theta=0よりC_1=0\\ x=0で\omega =0よりC_2=0 \] \[ \theta=\frac{1}{EI}\left(\frac{1}{6}qx^3-\frac{1}{4}qlx^2+M_Ax\right)\\ x=\frac{1}{2}l \ で \ \theta=0より \] \[\begin{align} \theta\big|_{x=\frac{1}{2}l} &=\frac{1}{EI}\left\{\frac{1}{6}q\left(\frac{l}{2}\right)^3-\frac{1}{4}ql\left(\frac{l}\\ {2}\right)^2+M_A\left(\frac{l}{2}\right)\right\}\\ &=0 \end{align}\] \[ \therefore M_A=\frac{1}{12}ql^2 \] $(4)$ \[ \omega =\frac{1}{EI}\left(\frac{1}{24}qx^4-\frac{1}{12}qlx^3+\frac{1}{24}ql^2x^2\right) \] $(5)$ \[ x=\frac{1}{2}lを代入する \] \[\begin{align} \omega\big|_{x=\frac{1}{2}l} &=\frac{1}{EI}\left\{\frac{1}{24}q\left(\frac{l}{2}\right)^4-\frac{1}{12}ql\left(\frac{l} {2}\right)^3+\frac{1}{24}ql^2\left(\frac{l}{2}\right)^2\right\}\\ &=\frac{ql^4}{384EI} \end{align}\]