Question: 12. (5 points) The solution to the square drumhead problem was (, y,t) = sin m=1 n=1 a (m x) sin (ny) [Emne )

12. (5 points) The solution to the square drumhead problem was (, y,t) = sin m=1 n=1 a (m x) sin (ny) [Emne ) [Emne wmnt + Fmne-iwmnt] with = = 22 mn (m n + a If a clamp is placed at the center of the drumhead requiring (x-1= )=0. a a 2 0, what are the first four distinct (and nonzero) vibrational frequencies of this drum- head? mn=1 mn=28 W = mn a Xw = TV ( + 1) = TV (22) = TV (2+2) = TV (22) mn=31 W3 = (2-2) - Hv (2) mn=4 wat TV + = TV (2) No reasoning.

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