Find the solution of the wave equation when initial velocity equal to O and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * Pu c². dx²

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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6:40
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Find the solution of the wave equation
when initial velocity equal to 0 and
initial deflection is (2kx/l) when x
between zero and (1/2) and deflection
equal to (2k(l-x)/I) when x between (1/2)
and (I) the P.D.E. is *
dt2
dx2
(n + 1) rct
-5 In
8k
u(x,1) =
(-1)"
(2n + 1) xx
sin
2 2n + 1
8k
u (x, t) =
(-1)"
(n + 1) xct
sin
(2n +1) xx
sin
=0 (2n + 1)2
--
Transcribed Image Text:6:40 a docs.google.com Find the solution of the wave equation when initial velocity equal to 0 and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * dt2 dx2 (n + 1) rct -5 In 8k u(x,1) = (-1)" (2n + 1) xx sin 2 2n + 1 8k u (x, t) = (-1)" (n + 1) xct sin (2n +1) xx sin =0 (2n + 1)2 --
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