11.5.2.4 Fourier method

Problem: Solve the wave equation on the given segment, with the boundary conditions \( V(0, t)==V(l, t)=0 \) and given initial conditions, using the Fourier method: \[ \begin{array}{l} V_{t t}^{\prime \prime}=121 V_{x x}^{\prime \prime} \\ V(x, 0)=\left\{\begin{array}{l} \frac{x}{7}, \quad 0 \leq x \leq 14 \\ \frac{28-x}{7}, \quad 14 \leq x \leq 28 \end{array} \quad V_{t}^{\prime}(x, 0)=0 .\right. \end{array} \]