Find the deflection u(x, t) of the string of length L = and c 2 =

Question:

Find the deflection u(x, t) of the string of length L = π and c² = 1 for zero initial displacement and “triangular” initial velocity u_t(x, 0) = 0.01x if 0 ≤ x ≤ 1/2π, u_t(x, 0) = 0.01(π - x) if 1/2π ≤ x ≤ π (Initial conditions with u_t(x, 0) ≠ 0 are hard to realize experimentally.)