For the beam shown below:

a$.$ Formulate the system of linear equations from the beam differential equation to

calculate deflection $(y),$ rotation $(\{$:$y^{\text{'}}),$ moment$(\{$:$y^{\text{'}\text{'}})$ and shear force$(\{$:$y^{\text{'}\text{'}\text{'}})$ along the

beam.

No marks will be given for utilizing the equations of statics.

b$.$ Determine the reactions using your answers from part a$).$

No marks will be given for utilizing the equations of statics.

c$.$ Plot the resulting $y,y^{\text{'}},y^{\text{'}\text{'}},$ and $y^{\text{'}\text{'}\text{'}}$ equations.

$L=8m$;$,M=55kN-m$;$,q=10k\frac{N}{m}$;$,E=1($assumed$),I=1($assumed$)$;