An elastic bar of length L spins with angular velocity w about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = wx. Due to this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: dx ((x)) + pa(x) = 0 PDE o(x) = Edu dx Hooke's law (1) where (x) is the axial stress in the rod, p is the mass density, and E is the (constant) Young's modulus. The bar is pinned on the rotation axis at x = 0, and it is free at x = L. 3 L X