1. Determine the displacement u(x; t) of systems modelled by the followingdifferential equationsazuazu(а);0 0ax?at2subject tou(x; t) = 0 ,u(n; t) = 0 ,t > 0auu(x; 0) = 0 ,= sinxIt=0ata2u(b)a²u;00ax2at2subject tou(x; t) = 0 , u(1; t) = 0 , t > 0u(x; 0) =ди= sinx ,= 0t=0at

The given initial-boundary value problem is of the form uxx=utt, 0<x<L,…

Determine the displacement u(x; t) of systems modelled by the following differential equations azu _ a?u (a) ;0 0 at2 subject to u(x; t) = 0, u(n; t) = 0 ,t > 0 u(x; 0) = 0, ди = sinx It%=0 at a2u a2u (b) ;0 0 subject to u(x; t) = 0 , u(1; t) = 0 , t > 0 u(x; 0) = au = sinx , = 0 t=0 at

Determine the displacement u(x; t) of systems modelled by the following differential equations azu _ a?u (a) ;0 0 at2 subject to u(x; t) = 0, u(n; t) = 0 ,t > 0 u(x; 0) = 0, ди = sinx It%=0 at a2u a2u (b) ;0 0 subject to u(x; t) = 0 , u(1; t) = 0 , t > 0 u(x; 0) = au = sinx , = 0 t=0 at

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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Question

1. Determine the displacement u(x; t) of systems modelled by the following
differential equations
azu
azu
(а)
;0<x <n , t> 0
ax?
at2
subject to
u(x; t) = 0 ,
u(n; t) = 0 ,t > 0
au
u(x; 0) = 0 ,
= sinx
It=0
at
a2u
(b)
a²u
;0<x<1 , t >0
ax2
at2
subject to
u(x; t) = 0 , u(1; t) = 0 , t > 0
u(x; 0) =
ди
= sinx ,
= 0
t=0
at

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