Recent content by usn7564

Explains why it wasn't elaborated further, feel silly now. Thank you, need to remind myself of BVP's it seems.

Sturm-Liouville problem: \frac{d}{dx} (r(x) \frac{dX}{dx}) + q(x)X(x) + \lambda p(x) X(x) = 0 \quad x \in \left[a, b \right] a_1 X(a) + a_2X'(a) = 0 b_1 X(b) + b_2X'(b) = 0 r, r', q, p \in \mathbb{C} \forall x \in in \left[a, b \right] Theorem: Under the additional condition that r(a)>0 (or...

Homework Statement Solve the BVP for a vibrating string with Separation of Variables/Fourier's method. \frac{\partial ^2}{\partial ^2 t} u(x,t) = c^2 \frac{\partial ^2}{\partial ^2 x} u(x,t) The string is of length L with each end fixed, ie u(0,t) = u(L,t) = 0 The Attempt at a Solution I...

Hey, I'm having some trouble understanding why the energy changes here between the blue and red paths (see attached image), it's representing state of an electron in a square lattice crystal. Like mathematically I can see it because obviously plug and chugging the different values k in E(k)...

Homework Statement Consider a chain with N >> 1 segments of length 1. One end of the chain is at the origin, the other at a point R. In this onedimensional model the segments may face left or right. The number of segments facing right is n. 1: What is the number of possible configurations in...

That worked, thanks.

Homework Statement A very big iron plate with the thickness 2h have, far from the plates edges, had a hole with the radius a drilled through it. With respect to the holes axis of symmetry the plate has a magnetization \bar{M} = M_0 \frac{a}{s} \hat{s} where s is the distance from the axis of...

Having some trouble getting any intuitive understanding from the wiki. What I was thinking (which may be way off) for the first image was that the spheres charges will rearrange so there are more positive charges on the right creating a dipole moment pointing in the same direction as the dipole...

Oh right of course, thank you.

Isn't that just for a dipole inside the sphere?

Homework Statement A dipole is placed next to a sphere (see image), at a large distance what is E proportional to? 3. The Attempt at a Solution or lack thereof I'm having trouble figuring out what's happening in any variations of these. How does the dipole affect the sphere's charge...

Didn't think of going backwards with the convolution theorem, that should certainly work thank you. Only half a year since I finished our course in complex analysis and the fact that I could use residues completely slipped my mind, thanks. Going to need to revise that a tiny bit, but was...

Homework Statement Doing some exam revision and one of the questions from an old exam has me stuck at the last step, simply need to inverse the following F( \omega ) = \frac{e^{i \omega}}{1+\omega ^2} We're allowed to use a table on the exams but I cannot find anything quite...

Homework Statement A circular disk with the mass m and radius r is hanging from two ropes with length l when suddenly the rope ED snaps. For this moment, find: a, The angular acceleration for the rope OB, the angular acceleration for the disk b, The force T acting in OB The Attempt at...

Obviously, Christ, should be the same as always except it's not a dot product anymore. Didn't feel like it was even part of my toolbox for some inexplicable reason. Should be able to figure out the rest now, thank you.