Chapter 9, Problem 9.4.2P

-2 A simple beam AB is subjected to a distributed load of intensity q(x) = q₀sin $\pi x$/L, where q₀is the maximum intensity of the load (see figure).

Derive the equation of the deflection curve, and then determine the deflection ${\delta }_{\max }$ at the midpoint of the beam. Use the fourth-order differential equation of the deflection curve (the load equation).