Boundary Conditions for Wave Solution

Classical Mechanics Level 3

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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