Chapter 7.9, Problem 23P

If a violin string is plucked (pulled aside and let go), it is possible to find a formula $f(x,t)$ for the displacement at time $t$ of any point $x$ of the vibrating string from its equilibrium position. It turns out that in solving this problem we need to expand the function $f(x,0),$ whose graph is the initial shape of the string, in a Fourier sine series. Find this series if a string of length $l$ is pulled aside a small distance $h$ at its center, as shown.