sec 4.7: Problem 3 Solve the wave equation with fixed endpoints and the given initial displacement and velocity. Utt = 4uxx, 0 < x < 7, t> 0 t>0 u(0,t)=0, u(7,t) = 0, u(x, 0) ut(x, 0) = = (0, 0 < x < 1/1 ½ < x < 7 [8, 금 5x(7x), 0 < x < 7 We solve the PDE using the series solution u(x,t) = sin (2) ( 7 2nπ 2nπ -bn sin t + cn cos 2nπ 7 7 ·t)). n=1 The coefficients b and c are Fourier coefficients we have computed many times: bn dx Cn = dx help (formulas) help (numbers)
sec 4.7: Problem 3 Solve the wave equation with fixed endpoints and the given initial displacement and velocity. Utt = 4uxx, 0 < x < 7, t> 0 t>0 u(0,t)=0, u(7,t) = 0, u(x, 0) ut(x, 0) = = (0, 0 < x < 1/1 ½ < x < 7 [8, 금 5x(7x), 0 < x < 7 We solve the PDE using the series solution u(x,t) = sin (2) ( 7 2nπ 2nπ -bn sin t + cn cos 2nπ 7 7 ·t)). n=1 The coefficients b and c are Fourier coefficients we have computed many times: bn dx Cn = dx help (formulas) help (numbers)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 34RE
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