Problem $1-$

A beam $($flexural rigidity $EI)$ is clamped at its left end and supported by a linear torsion spring

$($spring constant $k_T)$ at its right end as shown in the figure. THe beam is subjected to the moment

$M_0$ at the right end. Dtermine the following quantities in the beam:

a$)$ Deflection w

b$)$ Slope

c$)$ Shear force

d$)$ Bending moment

e$)$ Reaction force and moment

at $x=0.$

Hint. One method to solve the problem is to solve the ODE of the beam using proper boundary

conditions.