1. Consider the wave equation that describes the vibrating string with fixed ends J²u მ2 = J²u მ2 ди u(x, 0) = f(x); (x, 0) = g(x) Ət u(0,t) = u(L, t) = 0. Use its Fourier series solution u(x,t) u(x, t)=sin( to show that -Σsin ("7") [a, cos(x) + b, sin (TC)] n=1 u(x,t) = R(x-ct) + S(x + ct), where R and S are some functions. Hints: i. sin a cos b = 1 [sin(a + b) + sin(a − b)]. ii. sin a sin b [cos(a - b) - cos(a + b)]. L
1. Consider the wave equation that describes the vibrating string with fixed ends J²u მ2 = J²u მ2 ди u(x, 0) = f(x); (x, 0) = g(x) Ət u(0,t) = u(L, t) = 0. Use its Fourier series solution u(x,t) u(x, t)=sin( to show that -Σsin ("7") [a, cos(x) + b, sin (TC)] n=1 u(x,t) = R(x-ct) + S(x + ct), where R and S are some functions. Hints: i. sin a cos b = 1 [sin(a + b) + sin(a − b)]. ii. sin a sin b [cos(a - b) - cos(a + b)]. L
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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