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Consider a solution of the wave equation with c=1 on [0, l] with homogeneous Dirichlet or Neumann boundary conditions. (a) Show that its energy E=(1)/(2) ∫0^l(ut^2 ux^2) d x is a constant. (b) Let En(t) be the energy of its nth harmonic (the nth term in the expansion). Show that E=ΣEn. Hint: Use the orthogonality. Assume that you can integrate term by term.) | Numerade
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