/sci/ - Science & Math

[Anonymous No.4476381]

Hey /sci/, I have a question for you, if you can awnser, I will be forever in your debt and when my time comes, you will be mentioned!

Consider the the following system, composed off marbles with a mass m, linked with springs of a constant K and of lenght 'a' at rest. We consider the longitunidal movements.

Now, can you find the equation for the n'th marble?

Can you show that s(x,t)=s*sin(kx-wt) is a solution if (w^2)=((4K)/m)*(sin(Ka/2))^2

[Anonymous No.4476397]

This seems like the basic coupled problem for a solid state physics course.


This seems related

http://electron6.phys.utk.edu/qm2/modules/m5-6/periodic.htm

but I'm not sure.

Otherwise, maybe you find something of relevant in this infinite list of books

http://www.preterhuman.net/texts/science_and_technology/physics/

I can't be bothered with this, i.e. such nonlinear dispersion relations, right now (even if I'd love to understand graphen), but I guess the main idea is to writed down a next neightbor hamiltonian, then the matrix of equations of motions and diagonalize.

gl

[Anonymous No.4476402]

Its the wave equation I guess

The second derivative of s w.r.t time is equal to the second derivative of s w.r.t position multiplied by some factor with units of speed squared

[Anonymous No.4476420]

addon

okay, yes.
check out page 430 of

"Solid State Physics - Ashcroft, Neil W, Mermin, David N.djvu"

www.preterhuman.net/texts/science_and_technology/physics/State_of_Matter/Solid%20State%20Physics%20-
%20Ashcroft,%20Neil%20W,%20Mermin,%20David%20N.djvu