The beam shown in Figure $2\mathrm{.}1$ below is subjected to various loading conditions.

a$)$ Draw all necessary free$-$body diagrams using the method of section and find symbolic functions for the internal axial force $(N(x)),$ shear force $(V(x))$ and bending moment $(M(x))$ due to the external forces where $x$ is a horizonal coordinate along the length of each beam.

b$)$ Plot $N(x),V(x)$ and $M(x)$ using the numeric values given in each figure. For plotting, use your preferred software $($Matlab$,$ Excel, etc$).$ Note that you will lose points if you submit hand$-$drawn plots.

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Take $a=1\mathrm{.}3m$ and $=50$

Take $P=7kN,w_0=10k\frac{N}{m},$ and $M=10kNm.$