Problem 5 (sagging equilibrium. Haberman 4.2.1) Consider a deformation w. : [0, L] - [0, L] of a one-dimensional elastic continuum with constant equilibrium den- sity p > 0 and constant elasticity e with w.(0) = 0, w.(L) = L, and w. > 0. Let y : [0, L] - [-L, O] by y(x) = -w.(x) give a vertical representation of the deforma- tion. Assume w. is an equilibrium for the forced wave equation pullit = (Wxx + pg where g > 0 is a gravitational constant. (a) Find w. and determine conditions under which w. is admissible. Hint: Non- admissibility may arise is w.(x) @ [0, L] for some re (0, L) or if w.(x)