Consider a vibrating string of length L = π that satisfies the wave equation 4∂2u = ∂2u, 00. ∂x2 ∂t2
Assume that the ends of the string are fixed, and that the string is set in motion with no initial velocity from the initial position
u(x, 0) = 12 sin 2x − 16 sin 5x + 24 sin 6x. Find the displacement u(x, t) of the string.