The displacement of a uniform string stretched between x = 0 and x = L satisfies the wave equation, with boundary conditions y(0,t) = y(L,t) = 0. For t < 0, the string oscillates in its fundamental (lowest frequency but non-trivial) mode, and y(x,0) = 0. A musician strikes the midpoint of the string at t = 0, giving it a velocity kick, so that the change in the time derivative at t = 0 satisfies ∂y/∂t = X&(x - L/2). Find y(x,t) for t > 0.