Decay of sinusoidal velocity wave (kolmogorov flow)

[OldStudent0382]

Homework Statement

Find the velocity field u(x,t)

Homework Equations

\rho = constant
u(0,t)=0
u(0,L)=0

\frac{\partial u}{\partial t} = \nu \frac{\partial ^{2}u}{\partial x^{2}}

u(x,0)=U_{o}[sin(\frac{3\pi x}{L})+0.7sin(\frac{9\pi x}{L})]

The Attempt at a Solution

I have absolutely no idea how to start this problem (again) and I'm embarrassed to admit that I've been looking at it and searching for two hours -- and I have nothing to show for it.

Thank you in advance!

 

[OldStudent0382]

Would this be approached similarly to unsteady couette flow? I spent a few more hours trying to research the problem (and the topic) and I'm either not finding anything relevant or I'm just so far lost that I'm not finding the connection between this assignment and what I've been reading.