Question

Torsional vibration of a shaft is govened by e wave equation where e(z,t) is the anqular displacement (angle of twist) along the shaft, z is the distance from the end of the shaft and t is time. For a shaft of length that is supported by frictionless bearings at each end, boundary conditions are 0(0,t) 0(4x,t) 0, t> 0. Suppose that the initial angular displacement and angular velocity are e(z,0) 3cos(2r), 0(z,0)= 4+cos(2r), 0<z< 4m, respectively You may use the result that the eigenvalues of the boundary-value problem x" -X0, x'(0) = X' (4x)= 0 are n 0,1,2,3,... An= with corresponding eigenfunctions Xn cos find the final solution e(z,t) Use the method of separation c variables f still show as wrong with "How did I do?", so check your mark foo.) (It is possible to get half-marks for this question for a good but incomplete solution, However, half marks will e(z,t)

Answer 1

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