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Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) with the following boundary conditions: u(0, t)...

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Physics

Consider the 1D wave equation d^2u/dt^2 = c^2( d^2u/dx^2) withthe following boundary conditions: u(0, t) = ux (L, t) = 0 . (a)Use separation of variables technique to calculate the eigenvalues,eigenfunctions and general solution. (b) Now, assume L = π and c =1. With initial conditions u(x, 0) = 0 and ut(x, 0) = 1, calculatethe solution for u(x, t). (c) With initial conditions u(x, 0) =sin(x/2) and ut(x, 0) = 2 sin(x/2) − 3 sin(5x/2) calculate thesolution for u(x, t).

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