Chapter 5.2, Problem 7E

A cantilever beam of length L is embedded at its right end, and a horizontal tensile force of P pounds is applied to its free left end. When the origin is taken at its free end, as shown in Figure 5.2.8, the deflection y(x) of the beam can be shown to satisfy the differential equation

$EI{y}^{″}=Py-w(x)\frac{x}{2}.$

Find the deflection of the cantilever beam if w(x) = w₀x, 0 < x < L, and y(0) = 0, y′(L) = 0.

Figure 5.2.8 Deflection of cantilever beam in Problem 7