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 . Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. B. a c. k J²u 2²u 02-2 E. M. + = 0, 0 0 8²u Jx² ON. = 8²u Ət² 3 Əx² Ət Select ALL boundary/initial conditions that apply to this scenario | A. u(0, t) = L, t>0 |B. u(L, t) = 0, t> 0 du C. at 1-0 OD. (2,0) = 0, 0<2 0 Əx \z-L F. (0, t) = 0, t> 0 |G. u(x, L) = f(x), H. u(x,0) = f(x), 1. u(x,0)=L, 0 0 = f(x), 0 0 = 0, = f(x), 0 0 t>0 = 0, t>0
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 . Choose the PDE and boundary/initial conditions that model this scenario. Select the partial differential equation that can be used to model this scenario. B. a c. k J²u 2²u 02-2 E. M. + = 0, 0 0 8²u Jx² ON. = 8²u Ət² 3 Əx² Ət Select ALL boundary/initial conditions that apply to this scenario | A. u(0, t) = L, t>0 |B. u(L, t) = 0, t> 0 du C. at 1-0 OD. (2,0) = 0, 0<2 0 Əx \z-L F. (0, t) = 0, t> 0 |G. u(x, L) = f(x), H. u(x,0) = f(x), 1. u(x,0)=L, 0 0 = f(x), 0 0 = 0, = f(x), 0 0 t>0 = 0, t>0
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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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 .
Choose the PDE and boundary/initial conditions that model this scenario.
Select the partial differential equation that can be used to model this scenario.
B. a
c. k
J²u 2²u
02-2
E.
M.
+ = 0, 0<x<L,t> 0
8²u
Jx²
ON.
=
8²u
Ət²
3
Əx² Ət
Select ALL boundary/initial conditions that apply to this scenario
| A. u(0, t) = L, t>0
|B. u(L, t) = 0, t> 0
du
C.
at 1-0
OD. (2,0) = 0, 0<2<L
du
= 0, t> 0
Əx \z-L
F. (0, t) = 0, t> 0
|G. u(x, L) = f(x),
H. u(x,0) = f(x),
1. u(x,0)=L, 0<x<L
J.
du
du
Əxlt-0
OK. u(x, L)=L,
du
= 0,
dxx-0
du
Ət \x-L
du
Ət 17-0
0< <L,t> 0
= f(x), 0<x<L
0<x<L,t> 0
= 0,
= f(x), 0<x<L
0<x<L
0<x<L
0<x<L
t> 0
t>0
= 0, t>0
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