The height h(x, y) of an elastic sheet satisfies Laplace's equation in two dimensions 3² + a²h a²h ax ay = 0 The sheet is a rectangle with sides of length a in the x direction and length b in the y direction. The edges at x = 0 and x = a are held at zero height. The heights at the edges at y = 0 and y = b are fixed to the form h(x, 0)-h(x,b) = Hsin (20x) a (a) Sketch the boundary of the sheet, indicating which sides are held at zero and non-zero- height. (b) Using separation of variables, find h(x, y) in the range 0 ≤ x ≤ a, 0 ≤ y ≤ b.