Boundary conditons and initial conditions of a vibrating rod

1. Oct 5, 2007

yukawa

Finding the vibrational motion of a rod.

A uniform rod of lenght l is compressed from both ends so that its new lenght 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?

Last edited: Oct 5, 2007
2. Oct 5, 2007

Staff: Mentor

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.

3. Oct 5, 2007

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

Last edited: Oct 5, 2007
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