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A string of length L is secured at both ends. The string has no initial displacement, but has initial velocity f(z) at any point z. Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. 8²u du O A.k- ope OB. O C. a dr² 8²u 82² du OL- Du 8²u dt² Select ALL boundary/initial conditions that apply to this scenario A. u(z,0)=f(x), 0<=0 azz-0 OC. u(z, L) = f(z), 0<20 ди dr 1-0 du at -0 Ot-0 E. u(0, t)=L, t>0 OF. u(L, t)=0, t>0 OG. u(z,0)=L, du OH. Otx-L 00 = 0, 0 0 0 0 0² 012 W - <=0, t>0 dz-L J. u(0, t)-0, t>0 K. u(z,0)=0, 00 0

A string of length L is secured at both ends. The string has no initial displacement, but has initial velocity f(z) at any point z. Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. 8²u du O A.k- ope OB. O C. a dr² 8²u 82² du OL- Du 8²u dt² Select ALL boundary/initial conditions that apply to this scenario A. u(z,0)=f(x), 0<=0 azz-0 OC. u(z, L) = f(z), 0<20 ди dr 1-0 du at -0 Ot-0 E. u(0, t)=L, t>0 OF. u(L, t)=0, t>0 OG. u(z,0)=L, du OH. Otx-L 00 = 0, 0 0 0 0 0² 012 W - <=0, t>0 dz-L J. u(0, t)-0, t>0 K. u(z,0)=0, 00 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 string of length L is secured at both ends. The string has no initial displacement, but has initial velocity f(x) at any point z. Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. O A. k OB. O C. a² 8²u ди at 8²u dt² OH. = 0, 0<x<L,t> 0 8²u 8²u 0<=<L,t> 0 მე-2 81² Select ALL boundary/initial conditions that apply to this scenario A. u(x,0) = f(x), 0<x<L du B. = 0, t>0 ar-0 C. u(z, L) = f(x), 0<x<L ди D. <=0, t>0 ઈ-u dr² Ot0 E. u(0, t)=L, t>0 F. u(L, t)=0, t> 0 G. u(a,0)=L, du Ot-L 01. UN. 0<r<L,t> 0 ди dr L J. u(0, t)=0, t>0 art-0 du att-0 0<x<L <=0, t>0 K. u(x,0)=0, 0<x<L L. u(z, L)=L, 0<x<L ди M. -0, t>0 T f(x), 0<x<L f(x), 0<x<L.
Transcribed Image Text:A string of length L is secured at both ends. The string has no initial displacement, but has initial velocity f(x) at any point z. Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. O A. k OB. O C. a² 8²u ди at 8²u dt² OH. = 0, 0<x<L,t> 0 8²u 8²u 0<=<L,t> 0 მე-2 81² Select ALL boundary/initial conditions that apply to this scenario A. u(x,0) = f(x), 0<x<L du B. = 0, t>0 ar-0 C. u(z, L) = f(x), 0<x<L ди D. <=0, t>0 ઈ-u dr² Ot0 E. u(0, t)=L, t>0 F. u(L, t)=0, t> 0 G. u(a,0)=L, du Ot-L 01. UN. 0<r<L,t> 0 ди dr L J. u(0, t)=0, t>0 art-0 du att-0 0<x<L <=0, t>0 K. u(x,0)=0, 0<x<L L. u(z, L)=L, 0<x<L ди M. -0, t>0 T f(x), 0<x<L f(x), 0<x<L.
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