Determine a formula for the position u(x,t) each point x of the string at time t in the form of a trigonometric series. Also, determine a formula for the coefficients of the series for f and g.

a^2 \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 u}{\partial t^2} and 0<x<L; t>0

u(0,t) = 0; u(L,t) = 0; t>0

u(x,0) = f(x) and \frac{\partial u}{\partial t}(x,0) = 0

f(x) is continuous split and regular period 2L which describes the initial position of the string