Given an arbitrary harmonic solution to the wave equation

\[y(x,t) = A \sin (x-vt) + B \sin (x+vt),\]

find the general solution, i.e. find the coefficients \(A\) and \(B\) given the following boundary conditions:

\[y(0,t) = 0, \qquad y(L,0) = 1.\]

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