(ii) Use separation of variables to find the normal modes of the damped Wave Equation (1)...

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(ii) Use separation of variables to find the normal modes of the damped Wave Equation (1) subject to the BCs u (0, t) = 0 = u(l, t) (8) Impose a restriction on the parameters c, l, k which will guarantee that all solutions are oscillatory in time. You may assume that the eigenvalues and eigenfunctions are n²π² 12 Xn (x) = sin ηπ 1 n = 1, 2, 3... (ii) Use separation of variables to find the normal modes of the damped Wave Equation (1) subject to the BCs u (0, t) = 0 = u(l, t) (8) Impose a restriction on the parameters c, l, k which will guarantee that all solutions are oscillatory in time. You may assume that the eigenvalues and eigenfunctions are n²π² 12 Xn (x) = sin ηπ 1 n = 1, 2, 3...

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