Find dispersion relation using periodicity

1. Oct 11, 2009

Shafikae

Ok so heres another problem that i just completely dont understand at all. Thanks for your help.

A linear chain consists of 2N equally spaced identical particles with mass m and speration a, coupled by springs with alternating constands k1 and k2. Use the periodicity of the system to find the dispersion relation and sketch the resulting function ω (q). Hint: Assume

η2j = $$\alpha$$e^i[2jaq-ωt] , η2j+1 = βe^i[(2j+1)aq - ωt]

2. Oct 12, 2009

gabbagabbahey

What do η2j and η2j+1 represent? What does 'q' represent?

3. Oct 12, 2009

Shafikae

I dont know. This is what the professor assigned.

4. Oct 12, 2009

gabbagabbahey

How on Earth do you expect to show that η2j =$\alpha$ e^i[2jaq-ωt], if you have no idea what the variables η2j and 'q' represent?!