Use us (x, t) from part (a) to find the full solution u (x, t) to...

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Use us (x, t) from part (a) to find the full solution u (x, t) to the PDE (1), the BCs (2) and (3), and the ICs (4) and (5). Hint: use us (x, t) and u (x, t) to find a wave problem for some quantity v (x, t) that has Type I BCs (i.e. zero displacement) at x = 0, 1. Then write down D'Alembert's solution (without derivation) to satisfy the PDE and initial conditions for this problem (don't evalutate the integral in D'Alembert's solution). Then adjust D'Alembert's solution to handle the BCs at x = 0, 1. You don't need to evaluate the integral. Use us (x, t) from part (a) to find the full solution u (x, t) to the PDE (1), the BCs (2) and (3), and the ICs (4) and (5). Hint: use us (x, t) and u (x, t) to find a wave problem for some quantity v (x, t) that has Type I BCs (i.e. zero displacement) at x = 0, 1. Then write down D'Alembert's solution (without derivation) to satisfy the PDE and initial conditions for this problem (don't evalutate the integral in D'Alembert's solution). Then adjust D'Alembert's solution to handle the BCs at x = 0, 1. You don't need to evaluate the integral.

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