Show that the semi-infinite plate problem if the bottom edge of width 30 is held at...
Problem 3 (10 pts) The wavefunction of a particle in an infinite potential well, of width a, is initially given by 16 ?(x, t-0) sin"(? x/a) cos(nx/a) Find the expression for ?(x, t) for all t > 0
4. Consider the semi-infinite string problem given by Utt = cʻuza, 0<x< 0,> 0 u(x,0) = f(x), 0<x< ~ ut(2,0) = g(2), 0 < x < 0 u(0,t) = 0, t> 0 Suppose that c=1, f(0) = (x - 1) - h(2 – 3) and g(C) = 0. (a) Write out the appropriate semi-infinite d'Alembert's solution for this problem and simplify. (b) Plot the solution surface and enough time snapshots to demostrate the dynam- ics of the solution.
Problem #2 Two semi-infinite line currents lie on the z-axis in the regions -ODZ S -a and a S z<oo. Each carries a current I in the a direction. Calculate the magnetic field intensity H as a function ofρ and φ at z = 0.
In solving the particle in a one dimensional infinite depth box problem (0k x < a) we started with the function following is a true statement? (a) The value of k is found by requiring that the solution be normalized. (b) The function wx) is not an eigenfunciton of the operator d2/dx2 (c) It is necessary that this function equals a when x=0 (ie, Ψ(0) = a). (d) The boundary condition at x = 0 is used to show that...
I think it should be 9epslon e) The figure shows two semi-infinite media. One of the media is glass (x <0) and the other medium is a conductor (x >0). The two media have a common boundary at x -0. The electric field in glass is given by E, (4-3x +8x')ä, and the relative permitivity of glass is s,-2.25 From the given information we may conclude that the surface charge density equals: on the boundary 1) 46 2)-%, 3)-7.75E0 4)...
2. Solve the heat equation in 1 x 1 square with a = 1, U = 2- {1, if y 21, 10, if y<] The sides of the plate being held insulated. Mark the Answer sin na 0 4 = 2 Sin 2 e-n'r't cos (nty) o sin N sin 20-ni't cos (nty) + sin ma sin 2e" e-m’n’t cos (max) O 2 = n sin na in 2 e-nºn’t cos (nty) 1 Ou= o--** cos(17) n sin TL e...
Repeat the flat-plate momentum analysis by replacing the equation u(x, y) ~U ( ) 0<y>$(x) using a trigonometric profile approximation: 5 = sin()
Air at atmospheric pressure and 20 °C flows over a plate with the surface heat flux specified as 20 WImfor 0 <x < 15 cm 10 W/mo 15 cm. Derive the variation of wall temperature with the distance x from the leading edge in the laminar boundary layer region and evaluate the wall temperature numerically at 30 cm.
Problem 1. Make a sketch of the infinite strip 0< < 1. Then, find and sketch its image under the transformation w-12. În all these problems, z x + iy.
Consider the steady temperature T (2,y) in a rectangular plate that occupies 0 <<< 9 and 0 <y<5, which is heated at constant temperature 150 at 9 and 0 along its other three sides. (a) For separation solutions T(1,y) = F(x)G(y), you are given that admissible F(1) are the eigenfunctions Fn (1) = sinh(An I) for n=1,2,... and G(y) are the eigenfunctions Gn(y) = sin(Any) for n=1,2,... A for In = (b) The solution is the superposition T(z,y) = an...