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A semi-infinite string is located initially (at time t = 0) along the positive X-axis, 0 < x <∞. The string is looped around a vertical support at the 'far end', corresponding to x → ∞o, which exerts no vertical force on the tape: limu(x, t) = 0. At the near end, corresponding to x = 0, the tape is tethered to a support, which fixes its position. The initial velocity is zero throughout the tape, i.e., at ди t = 0, = 0. at ²u The displacement u(x, t) of the string obeys the wave equation - A t, where c is a at² given positive constant with units m s¹, and A is a given positive constant with units m s ³. Solve the PDE analytically for the displacement of the tape at any location at any time t > 0. = c². ² əx²

A semi-infinite string is located initially (at time t = 0) along the positive X-axis, 0 < x <∞. The string is looped around a vertical support at the 'far end', corresponding to x → ∞o, which exerts no vertical force on the tape: limu(x, t) = 0. At the near end, corresponding to x = 0, the tape is tethered to a support, which fixes its position. The initial velocity is zero throughout the tape, i.e., at ди t = 0, = 0. at ²u The displacement u(x, t) of the string obeys the wave equation - A t, where c is a at² given positive constant with units m s¹, and A is a given positive constant with units m s ³. Solve the PDE analytically for the displacement of the tape at any location at any time t > 0. = c². ² əx²

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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A semi-infinite string is located initially (at time t = 0) along the positive X-axis, 0 < x < ∞ . The string is looped around a vertical support at the 'far end', corresponding to x→ ∞, which exerts no 0, the tape is Ә vertical force on the tape: limu(x, t) = 0. At the near end, corresponding to x = х→00 дх tethered to a support, which fixes its position. The initial velocity is zero throughout the tape, i.e., at ди t = 0, = 0. at อใน əx² The displacement u(x, t) of the string obeys the wave equation A t, where c is a given positive constant with units m s´¹, and A is a given positive constant with units m s ³. Solve the PDE analytically for the displacement of the tape at any location at any time t > 0. ²u at² C²
Transcribed Image Text:A semi-infinite string is located initially (at time t = 0) along the positive X-axis, 0 < x < ∞ . The string is looped around a vertical support at the 'far end', corresponding to x→ ∞, which exerts no 0, the tape is Ә vertical force on the tape: limu(x, t) = 0. At the near end, corresponding to x = х→00 дх tethered to a support, which fixes its position. The initial velocity is zero throughout the tape, i.e., at ди t = 0, = 0. at อใน əx² The displacement u(x, t) of the string obeys the wave equation A t, where c is a given positive constant with units m s´¹, and A is a given positive constant with units m s ³. Solve the PDE analytically for the displacement of the tape at any location at any time t > 0. ²u at² C²
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