Question

Write the initial-boundary value problem for small vibrations of a string. Both ends of the string are fastened at certain heights. The string is heavy so the gravitation force should be included.

Answer 1

So far for the boundary conditions I have:
u(L,t)=h1(t)
U(0,t)=h2(t) since each side of the string is fixed at some height where L is the length of the string