3. The equation y" = -X²y, for some real number A, represents the waveform of a vibrating string with frequency A. (a) Show that y(x) = A sin(Ar) + B cos(Ar) is always a solution to this equation. (b) Which values of A and B fit the initial condition y(0) = 0? (c) Suppose our string has length L and is clamped at both ends, so that y(0) = 0 and y(L) = 0, and suppose we have a nonzero solution y(x) = A sin(Ax) + B cos(Ax). Explain why we must have X= 1 for some natural number n.' %3D

3. The equation y" = -X²y, for some real number A, represents the waveform of a vibrating string with frequency A. (a) Show that y(x) = A sin(Ar) + B cos(Ar) is always a solution to this equation. (b) Which values of A and B fit the initial condition y(0) = 0? (c) Suppose our string has length L and is clamped at both ends, so that y(0) = 0 and y(L) = 0, and suppose we have a nonzero solution y(x) = A sin(Ax) + B cos(Ax). Explain why we must have X= 1 for some natural number n.' %3D

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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