I have the following PDE, how ever I do not know much about PDEs.

I am more an ODE guy. I would be glad if you can give me directions and/or

references for attacking the following equation

$\displaystyle \displaystyle \frac{\partial^2u}{\partial t^2}=-c^2\frac{\partial^4 u}{\partial x^4}$

which represents the motion of an elastic bar of length $\displaystyle L$

with a fixed end at $\displaystyle 0$ and the other one is free.

It reminds me the heat equation when I factor this into components as

$\displaystyle \displaystyle (D_t-icD_x^2)(D_t+icD_x^2)u=0$,

how ever the coefficients are complex valued.

I believe there should be another way.