Find dispersion relation using periodicity

[Shafikae]

Ok so here's another problem that i just completely don't 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

η_2j = $$\alpha$$e^i[2jaq-ωt] , η_2j+1 = βe^i[(2j+1)aq - ωt]

 

[gabbagabbahey]

What do η_2j and η_2j+1 represent? What does 'q' represent?

 

[Shafikae]

I don't know. This is what the professor assigned.

 

[gabbagabbahey]

Ask your professor then.

How on Earth do you expect to show that η_2j =$\alpha$ e^i[2jaq-ωt], if you have no idea what the variables η_2j and 'q' represent?!