- #1

A.Magnus

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Consider the wave equation with homogeneous Neumann-Dirichlet boundary conditions:

##\begin{align}

u_{tt} &= c^2U_{xx}, &&0<x<\mathscr l, t > 0\\

u_x(0, t) &=u(\mathscr l, t) = 0, &&t > 0\\

u(x, 0) &=f(x), &&0<x< \mathscr l\\

u_t(x, 0) &=g(x), &&0<x< \mathscr l

\end{align}##

(a) Give a physical interpretation for each line in the problem above.u_{tt} &= c^2U_{xx}, &&0<x<\mathscr l, t > 0\\

u_x(0, t) &=u(\mathscr l, t) = 0, &&t > 0\\

u(x, 0) &=f(x), &&0<x< \mathscr l\\

u_t(x, 0) &=g(x), &&0<x< \mathscr l

\end{align}##

(b) State the eigenvalue problem for ...

(c) ...

(d) ...

I am posting this asking for help on answering (a) since I do not have background whatsoever in either engineering or physics. I know how to work out the rest of questions after (a), since they are all math questions.

Thank you very much for your time and help.