Please give some insight on how to apply boundary conditions. This is really important for me to understand separation of variables and how/which terms are eliminated and why.
Please give some insight on how to apply boundary conditions. This is really important for me to understand separation o...
I am hoping with explanation to go with solving the problem, especially with regards to applying the boundary conditions correctly. Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar Problem 2 Find the solution to V2 Y(r, e, ø) = 0 inside a sphere with the following boundary conditions: aw (1, e, ) sin20 cosp = ar
Find the solution to ∇2 Ψ(r, θ, φ) = 0 inside a sphere with the following boundary conditions: ∂Ψ (1,θ,φ)=sin2θcosφ.∂r Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar
Find the solution to inside a sphere with the following boundary conditions applied to its three sides. Please give explanation. Find the solution to V24(r, e, ¢) = 0 inside a sphere with the following boundary conditions: (1, e, ) sin20 cosp ar
Apply separation of variables and solve the following boundary value problem 0 < x < t> 0 t>O Ytt(x, t) = 25 yxx(x, t) ya(0,t) = y2(7,t) = y(x,0) = f(x) yt(x,0) = g(x) 0 << 0 <r<a
please help me solve all the question. please. thank you. Question 3. Separation of variables. Consider Laplace's Equation in two dimensions:-+-- (a) Write φ(z y) F(x)G(y) and use separation of variables to get ordinary differential equa- tions for F and CG (b) Consider the rectangular region ((r,y) E R:0 conditions on Φ < a, 0 y b with three boundary 0(x, 0) = 0, D(x, b) = 0, (0,y) = 0 Obtain conditions on F and G on those boundaries...
Question 3. Separation of variables Consider Laplace's Equation in two dimensions (a) Write Ф(r,y)-F(x)G(y) and use separation of variables to get ordinary differential equa- tions for F and G (b) Consider the rectangular region {(x, y) E R2: 0Ka, 0 y b with three boundary conditions on Ф об obtain conditions on F and G on those boundaries where conditions on Ф are given (c) (i) Solve the differential equations found in (a), subject to the conditions found in (b)...
Question 3. Separation of variables. Consider Laplace's Equation in two dimensions: (a) Write Φ(x,y) F(x)G(y) and use separation of variables to get ordinary differential equa- tions for F and G (b) Consider the rectangular region {(x,y) є R2 : 0 a, 0-y-b} with three boundary x conditions on Ф: obtain conditions on F and G on those boundaries where conditions on Ф are given. (c) (i) Solve the differential equations found in (a), subject to the conditions found in (b)...
Q1. SEPARATION OF VARIABLES - SPHERICAL SIGMA The surface charge density on a sphere (radius R) is a constant, σ0 (As usual, assume V(r = ∞) = 0, and there is no charge anywhere inside or outside, it's ALL on the surface!) i) Using the methods of section 3.3.2 (i.e. explicitly using separation of variables in spherical coordinates), find the electrical potential inside and outside this sphere. ii) Discuss your answer, explain how you might have just "written it down"...
Problem 3. Show that the solution of the partial differential equation (Laplace equation), Wxx(x, y) + Wyy(x, y) = 0, with the four boundary conditions: w(x,0) = 0, w(x, 1) = 0, w(0, y) = 0 and w(1, y) = 24 sin ny, can be obtained as w(x, y) = 2 sinh nx · sin ny. [Suggested Solution Steps for Problem 3] (1) Apply the method of separation of variables as w(x,y) = X(x) · Y(y); (2) substitute into the...
Please give me a detailed answer, I really need to understand how to do this problem. Thank you. 4. A bob on a 1 m long string is rotated in vertical cirele. When the bob is in the position when the string makes 10° angle below horizontal, its centripetal acceleration is 20 m/s'. Find tangential acceleration at this point and speed of the bob in the bottom point of the circle.