Question

PDE's: A string has its ends fixed at x=0 and x=L. It is displaced a distance h at its midpoint and then released. Formulate a boundary value problem for the displacement y(x,t) of any point x of the string at time t.

Answer 1

Here's what I got: Let y = y=(x,t) and a^2=tau/mu. Then y_tt = a^2(y_xx) and y(L/2,0)=h, y_t(x,0)=0, y(0,t)=0, y(L,t)=0.

Please confirm if this is correct or not.

Answer 2

Looks right to me.

Answer 3

Thank you.