Exercise 9 Show that the boundary conditions, (14), require that Ak = k1 = Ck =...

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Exercise 9 Show that the boundary conditions, (14), require that Ak = k1 = Ck = 0, m/a, m =1, 2, 3, k2 = n/b, n = 1, 2, 3, (27) Explain why negative integer or zero values for m and n are not relevant or do not contribute under the given boundary conditions. Given the results of this exercise, we can, by redefining some of the coefficients, write the solution as sin (max) sin (n) [Emn exp(iwmnt)+Fmn exp(iwmnt)], (28) Z (x, y, t) = sin m=1 n=1 where mn = (m n2 + 62 (29) The drumhead is held stationary by the rim, and so the boundary conditions are; Z(0, y, t) = Z (x, 0, t) = Z(a, y, t) = Z (x, b, t) = 0, (14) Exercise 9 Show that the boundary conditions, (14), require that Ak = k1 = Ck = 0, m/a, m =1, 2, 3, k2 = n/b, n = 1, 2, 3, (27) Explain why negative integer or zero values for m and n are not relevant or do not contribute under the given boundary conditions. Given the results of this exercise, we can, by redefining some of the coefficients, write the solution as sin (max) sin (n) [Emn exp(iwmnt)+Fmn exp(iwmnt)], (28) Z (x, y, t) = sin m=1 n=1 where mn = (m n2 + 62 (29) The drumhead is held stationary by the rim, and so the boundary conditions are; Z(0, y, t) = Z (x, 0, t) = Z(a, y, t) = Z (x, b, t) = 0, (14)

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To show that the boundary conditions 14 require A12 Ck2 0 we start with the general solution of the ... View the full answer