9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a...
7. Solve the vibrating membrane problem (symmetric case) 11(a,t) = 0 u(r,0) = f(r) u,(r, 0) = g(r) a) a = 1, c = 1, i(r) = Jo(air), g(r) = 0. b) a = 1, c = 1, f(r) = Jo(U3r), g(r) = 1-r'. 7. Solve the vibrating membrane problem (symmetric case) 11(a,t) = 0 u(r,0) = f(r) u,(r, 0) = g(r) a) a = 1, c = 1, i(r) = Jo(air), g(r) = 0. b) a = 1, c...
Solve the circularly symmetric vibrating membrane PDE given as u_tt = ∇^2*u BC : u(1, θ, 0) = 0, 0 < t < ∞ ICs : u(r, θ, 0) = J_0*(2.4r) − 0.25*J_0*(14.93r), 0 ≤ r ≤ 1 u_t(r, θ, 0) = 0 Solve the circularly symmetric vibrating membrane PDE given as Utt = Dau BC : u(1,0,0) = 0, 0<t< oo ICs : u(r,0,0) = J.(2.4r) – 0.25J(14.93r), 0 <r <1 Ut(r,0,0) = 0
1- Consider waves propagating in a vibrating quarter-circular membrane: at2 The displacement u(r, e t) is zero on the entire boundary at all times. a) Write down explicitly the three boundary conditions expressed above. b) Starting by the method of separation of variables, find the solution and show that it is given by ui (r, θ' t) = Σι Σ J1(A ct) sinde) [A, cos(JA Ct)+B, sin(vA ct)], where l is a positive even integer, and n is a positive...
7. (1 point) For r-f (θ)-sin(θ)-1: (A) Find the area contained within f() (B) Find the slope of the tangent line to f(9) at-0. 7. (1 point) For r-f (θ)-sin(θ)-1: (A) Find the area contained within f() (B) Find the slope of the tangent line to f(9) at-0.
3. (a) Solve the boundary value problem on the wedge u(r, 0) = 0 0<r<p, a(r, g) = 0 0<r<p, u(p, 0)-/(0), 0 < θ < θο. (b) State the mathematical and physical boundary conditions for this problem. (c) Suppose ρ-1.00-π/3, and f(9)-66ere. Plot the solution surface and polar contour plot for N -10 3. (a) Solve the boundary value problem on the wedge u(r, 0) = 0 0
5. Solve Au=0, r>1, 0 < θ < 2π, a(1,0) cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
5. Solve Au=0, r>1, 0 < θ < 2π, u(1.0) = cos θ, 0 < θ < 2π. 5. Solve Au=0, r>1, 0
Solve the following problem อน a( 1,0) = 0, a(2,0) = f(0), 0 < θ <う
All of them please if you can 6. Solve the Dirichlet problem 0<r<3 la(3.0) = 1-cos0+ 2 sin 20. θ < 2π 0 7. Solve the Dirichlet problem lu(3,0) = 3-2 sin θ + cos 20, θ 0 2π 8. Solve the Dirichlet problem a(3,0) 2 + sin 20, 0 θ<2π 6. Solve the Dirichlet problem 0
Solve the Dirichlet problem in an infinite strip uxx + uyy=0 for x ϵ R and 0 <y <b , u(x,0)=f(x) , u(x,b)=g(x). (Hint: first do the case f=0. The case g=0 reduces to this one by the substitution y→ b-y , and the case general is obtained by superposition) 4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g...