11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a ring that is free to slide up and down a vertical pole. One can show that under these assumptions the tangent line to the free end will always be horizontal. Separate variables and describe the motion of the string at any time t> 0, given any initial shape and (vertical) velocity. Positioning the string along the interval [0, L] of the x-axis, solve the boundary value problem by separation of variables. Utt = c²uxx, 0 < x 0 ur(0,t) = u(L,t)=0, t>0 u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L
11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a ring that is free to slide up and down a vertical pole. One can show that under these assumptions the tangent line to the free end will always be horizontal. Separate variables and describe the motion of the string at any time t> 0, given any initial shape and (vertical) velocity. Positioning the string along the interval [0, L] of the x-axis, solve the boundary value problem by separation of variables. Utt = c²uxx, 0 < x 0 ur(0,t) = u(L,t)=0, t>0 u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L
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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![11. An ideal elastic string of length L is fixed at its right end, but its left end is
attached to a ring that is free to slide up and down a vertical pole. One can
show that under these assumptions the tangent line to the free end will always
be horizontal. Separate variables and describe the motion of the string at any
time t > 0, given any initial shape and (vertical) velocity. Positioning the
string along the interval [0, L] of the x-axis, solve the boundary value problem
by separation of variables.
Utt = c²uxx, 0 < x <L, t>0
ur(0,t) = u(L,t)=0, t>0
u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2fb781f-b8bd-4fad-b6b5-df8a03e91532%2F2a79b0ed-41dc-4d0d-b911-e0f519a320a1%2Fih001zb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11. An ideal elastic string of length L is fixed at its right end, but its left end is
attached to a ring that is free to slide up and down a vertical pole. One can
show that under these assumptions the tangent line to the free end will always
be horizontal. Separate variables and describe the motion of the string at any
time t > 0, given any initial shape and (vertical) velocity. Positioning the
string along the interval [0, L] of the x-axis, solve the boundary value problem
by separation of variables.
Utt = c²uxx, 0 < x <L, t>0
ur(0,t) = u(L,t)=0, t>0
u(x, 0) = f(x), ut(x,0) = g(x), 0 < x < L
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