Chapter 14.2, Problem 3E

The displacement of a semi-infinite elastic string is determined from

$a^2\frac{{\partial }^{2}u}{\partial x^2}=\frac{{\partial }^{2}u}{\partial t^2},x>0,t>0$

$u(0,t)=f(t),\underset{x\to \infty }{\lim }u(x,t)=0,t>0$

$u(x,0)=0,{\frac{\partial u}{\partial t}|}_{t-0}=0,x>0$.