Boundary conditons and initial conditions of a vibrating rod

[yukawa]

Finding the vibrational motion of a rod.


A uniform rod of length l is compressed from both ends so that its new length becomes l(1-2 $$\epsilon$$). The compression force is then removed and the rod is left to vibrate freely. Find the subsequent vibrational motion of the rod.


What are the initial conditions and boundary conditions for this question?

 

[Astronuc]

One can treat this like a spring which is compressed and released.

Initial condition would be either the initial length or displacement from unloaded length.

 

[yukawa]

Is the following correct?

BC: partial(x)/partial(u)= 0 at x=0 and x= l

IC: u(x,0) = 2(epsilon)l , partial(u)/partial(t)=0 at t=0