1- Consider waves propagating in a vibrating quarter-circular membrane: at2 The displacement u(r,...
Using Laplace Equation PDE
42.(a) Solve for u(r, e): That is, the region is an annulus betweenr 1 andr 2. HINT: First draw a picture of it, to get a look at the problem. Now, you should be able to readily get Then, see that you have 27-periodicity, so K n (n-1, 2, ) and D-0, so u (r, θ) A' + B' In r + an infinite series with r's and θ's in it. But look at your picture:...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...