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A magnetic field with an intensity Fo cos (2wt) (F, and w are positive constants) is applied to an initially stationary L-length strand, fixed at both ends. The mathematical model for the field of displacement u (x, t) of points on the wire is given below. a?u(x,t) %3D a?u(x,t) + Fo cos(2wt), 0 0 at2 ax2 Boundary Conditions; u(0, t) = 0, t >0 ди(L,t) 0, t>0 %3D дх Starting Conditions u(x,0) = 0, 0 < x < L ди(х,0) = 0, 0

A magnetic field with an intensity Fo cos (2wt) (F, and w are positive constants) is applied to an initially stationary L-length strand, fixed at both ends. The mathematical model for the field of displacement u (x, t) of points on the wire is given below. a?u(x,t) %3D a?u(x,t) + Fo cos(2wt), 0 0 at2 ax2 Boundary Conditions; u(0, t) = 0, t >0 ди(L,t) 0, t>0 %3D дх Starting Conditions u(x,0) = 0, 0 < x < L ди(х,0) = 0, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A magnetic field with an intensity Fo cos (2wt) (Fo and w are positive constants) is applied to an initially stationary L-length strand, fixed at both ends. The mathematical model for the field of displacement u (x, t) of points on the wire is given below. a?u(x,t) c2 a?u(x,t) + Fo cos(2wt), 0 <x <L , t>0 at? Boundary Conditions; u(0, t) = 0, t>0 ди(L,t) = 0, t>0 %3D Starting Conditions u(x, 0) = 0, 0 <x < L ди(х,0) = 0, 0 <x < L %3D at Find the general solution of the partial differential wave equation defined as the initial and boundary value problem by applying the Laplace transform method in the domain ū (x, s).
Transcribed Image Text:A magnetic field with an intensity Fo cos (2wt) (Fo and w are positive constants) is applied to an initially stationary L-length strand, fixed at both ends. The mathematical model for the field of displacement u (x, t) of points on the wire is given below. a?u(x,t) c2 a?u(x,t) + Fo cos(2wt), 0 <x <L , t>0 at? Boundary Conditions; u(0, t) = 0, t>0 ди(L,t) = 0, t>0 %3D Starting Conditions u(x, 0) = 0, 0 <x < L ди(х,0) = 0, 0 <x < L %3D at Find the general solution of the partial differential wave equation defined as the initial and boundary value problem by applying the Laplace transform method in the domain ū (x, s).
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