Question

can you show details about the all of the answers for this question? thanks

Torsional vibraton of a shat is govemed by the wave equation, &2 where ,t) is the angular 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 3r that is supported by frictionless bearings at each end, the boundary conditions are (0,)-(3,t)-, t>0. Suppose that the initial angular displacement and angular velocity are ,0)-cos(4r), 8,0)-6+3con(4), 0czc3, respectively You may use the result that the eigenalues of the boundary-value problem x'0)-x' ( ) - 0 x-Ax- are -0,1,2,3, with comesponding eipantunctions Xnmcon Use the method of separation of variables to find the fieal soluson a,t). ( is possible to get half-marks for this question for a good but incomplete solution. However, half marks will still show as wrong with "How dd I do?, so check your mark too.) z,4) om the end of the shaft and t is time. Fora shaft of length 3r that is supported by frictioni 0(0,t)=0z(3m,t)=0, t>0. e(z,0) = cos(4z), (=, 0) = 6 + 3cos(4z), 0

Answer 1

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