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D) Consider the following expressions for the initial conditions: f(x) = 0 and g(x) = ) = 0 and g(x) = x²(x−L) 4 Po f?? sin(??) Hint the fourier coefficient takes the form: L Zn Write the following values used in the first two terms of the expansion An= Bn= X

D) Consider the following expressions for the initial conditions: f(x) = 0 and g(x) = ) = 0 and g(x) = x²(x−L) 4 Po f?? sin(??) Hint the fourier coefficient takes the form: L Zn Write the following values used in the first two terms of the expansion An= Bn= X

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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answer the folling in d

D) Consider the following expressions for the initial conditions: f(x) = 0 and g(x) = ) = 0 and g(x) = x²(x−L) 4 Po f?? sin(??) Hint the fourier coefficient takes the form: L Zn Write the following values used in the first two terms of the expansion An= Bn= X
Transcribed Image Text:D) Consider the following expressions for the initial conditions: f(x) = 0 and g(x) = ) = 0 and g(x) = x²(x−L) 4 Po f?? sin(??) Hint the fourier coefficient takes the form: L Zn Write the following values used in the first two terms of the expansion An= Bn= X
Consider the problem of damped vibration of an elastic string, governed by: ди Ju 2²u Po = To -ß- ƏR² 2²u 2x² -, subject to the following boundary and initial conditions: u(0,t) = u(L,t) = 0, u(x,0) = f(x), Ət Ət n = ∞ Zn • Derive a series solution of the from u(x,t) = Σ • Σ A,sin( 20 ) + B, cos ( 20 )|sin(x,x) t+B n = ??L • Express Z, and K, in terms of To, Po, ß, L, n and π. -(x,0) = g(x)
Transcribed Image Text:Consider the problem of damped vibration of an elastic string, governed by: ди Ju 2²u Po = To -ß- ƏR² 2²u 2x² -, subject to the following boundary and initial conditions: u(0,t) = u(L,t) = 0, u(x,0) = f(x), Ət Ət n = ∞ Zn • Derive a series solution of the from u(x,t) = Σ • Σ A,sin( 20 ) + B, cos ( 20 )|sin(x,x) t+B n = ??L • Express Z, and K, in terms of To, Po, ß, L, n and π. -(x,0) = g(x)
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