(Solved): Problem 1: The beam below has bending rigidity \( E I \) and is subjected to a concentrated load o ...

Problem 1: The beam below has bending rigidity \( E I \) and is subjected to a concentrated load of intensity \( P \) at \( \mathrm{B} \) (i.e. at \( x=L \) ). The beam is on a roller support at \( \mathrm{A} \), while the support at \( \mathrm{C} \) permits vertical translation, but prohibits rotation and horizontal translation. Using the second order differential equation, derive the deflection \( v \) as a function of \( x \) throughout the length of the beam.