If an elastic string is free at one end, the boundary condi tion to be satisfied there is that u0. find the displacement u(x, t) in an elastic string of length l, fixed at x = 0 and free at x = l, set in motion with no initial velocity from the initial position u(x,0) f(x), where f is a given function. hint: show that the fundamental solutions for this problem, satisfying all conditions except the nonhomogeneous initial condition, are
where λ-1)π/2l, n 1, 2, .
compare this prob- lem with problem 23 of section 11.1; pay particular attention to the extension of the initial data out of the original interval o, l