Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1 A taut string of length 3 with ends constrained on the x-axis at x-0 and x-5 is released from its central position with initial velocity defined by f(x)= 2, for 00 subject to the boundary conditions ди (0,t)=0 and u(5,t)=0 for t>0 and the initial conditions и (х,0) - 0 , for 0l=10 4) There will be no constant term in HRFCS of o(x) (i.e., the estimated coefficient ao will be zero)

1 A taut string of length 3 with ends constrained on the x-axis at x-0 and x-5 is released from its central position with initial velocity defined by f(x)= 2, for 00 subject to the boundary conditions ди (0,t)=0 and u(5,t)=0 for t>0 and the initial conditions и (х,0) - 0 , for 0l=10 4) There will be no constant term in HRFCS of o(x) (i.e., the estimated coefficient ao will be zero)

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
See similar textbooks
icon
Related questions
Question
1 A taut string of length 3 with ends constrained on the x-axis at x-0 and x-5 is released from its central position with initial velocity defined by f(x) = 2, for 0<x<5 The subsequent displacement u(x,f) at time f and a distance x from the left end is governed by the wave equation a?u 1 a?u 9 ôr? 0<x<5, t>0 subject to the boundary conditions ди (0,t)=0 and u(5,t)=0 for t>0 ôx and the initial conditions u(x,0)= 0 , for 0<x<5 ôu (x,0)= f (x) , for 0<x<5 ốt Find the expression for the subsequent displacement u(x,t) in the string. Hint: Use the auxiliary function g(x) which is extension of fx) into the interval from 0 to 10: fs(x)=2, (F(10-x)=-2, 5<x<10 0<x<5 g(x)= 8(x): Let ø(x) be an even periodic extension of g(x). Then, o(x) will have the following properties: 1) 9(x)=g(x)=f(x), 0<x<5 2) 9(x) can be expanded into HRFCS. 3) The period of ø(x) is T=21=20=>l=10 4) There will be no constant term in HRFCS of 9(x) (i.e., the estimated coefficient ao will be zero)
Transcribed Image Text:1 A taut string of length 3 with ends constrained on the x-axis at x-0 and x-5 is released from its central position with initial velocity defined by f(x) = 2, for 0<x<5 The subsequent displacement u(x,f) at time f and a distance x from the left end is governed by the wave equation a?u 1 a?u 9 ôr? 0<x<5, t>0 subject to the boundary conditions ди (0,t)=0 and u(5,t)=0 for t>0 ôx and the initial conditions u(x,0)= 0 , for 0<x<5 ôu (x,0)= f (x) , for 0<x<5 ốt Find the expression for the subsequent displacement u(x,t) in the string. Hint: Use the auxiliary function g(x) which is extension of fx) into the interval from 0 to 10: fs(x)=2, (F(10-x)=-2, 5<x<10 0<x<5 g(x)= 8(x): Let ø(x) be an even periodic extension of g(x). Then, o(x) will have the following properties: 1) 9(x)=g(x)=f(x), 0<x<5 2) 9(x) can be expanded into HRFCS. 3) The period of ø(x) is T=21=20=>l=10 4) There will be no constant term in HRFCS of 9(x) (i.e., the estimated coefficient ao will be zero)
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS