Question 4 (30 marks): Consider a beam with clamped ends at x = 0 and x = L. A concentrated load P is applied at the point x = L/3. The differential equation describing the deflection y is given as: dx4 x EI y(0) = 0, y'(0) = 0, y(L) = 0, y'(L) = 0 where 8 is the Dirac delta function. Find the deflection of the beam, y(x), subject to the point load. Hints: (i) assume y"(0) = C, and y""(0) = C2, and obtain the solution form of y in terms of C1 and C2 using Laplace transform. (ii) find the constants C, and C2 by boundary conditions at x = L, and hence determine the final form of y. P X N V