Question

where (x, t) is the angular displacement (ang le of twist) along the shaft, x is the distance from the end of the shaft and t is time. For a shaft of length 4m that is supported by frictionless bearings at each end, the boundary conditions are t 0. Өx (0, г) — Өx(4л, t) — 0, Suppose that the initial angular displacement and angular velocity are Of(x, 0) = 2 cos(3x) = 6 cos(4x), ex, 0) 0 x< 4 respectively. You may use the result that the eigenvalues of the boundary-value problem х! — АХ — 0, x'(0) = x' (4) = 0 are п %3D 0, 1, 2, 3, ... An - 42 with corresponding eigenfunctions Xn = cos Use the method of separation of variables to find the final solution O(x, t).

Answer 1

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