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

it's a second order differential equation
and the boundary conditions are
y(0)=y(l)=0
the equation is
y''(x)=f
where f is the force