Consider 2u/t2 = c22u/x2 with the boundary conditions u = 0 at x = 0 m2u t2 = T0 u x ku
Chapter 5, Problem 5.8.12(choose chapter or problem)
Consider 2u/t2 = c22u/x2 with the boundary conditions u = 0 at x = 0 m2u t2 = T0 u x ku at x = L. (a) Give a brief physical interpretation of the boundary conditions. (b) Show how to determine the frequencies of oscillation. Estimate the large frequencies of oscillation. (c) Without attempting to use the Rayleigh quotient, explicitly determine if there are any separated solutions that do not oscillate in time. (Hint: There are none.) (d) Show that the boundary condition is not self-adjoint: that is, show L 0 un d2un dx2 um d2un dx2 dx = 0 even when un and um are eigenfunctions corresponding to different eigenvalues.
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