Unformatted text preview: b. Find the R equation and show that it has the general solution R = c 1 sin + c 2 cos . c. Find a numerical value for the smallest frequency of free vibration . 2. The vibrations of a rectangular membrane are governed by the PDE: 2 u t 2 = 2 u x 2 + 2 u y 2 , x 1 , y 2 (4) The four edges of the membrane are held xed with displacement u = 0. Use separation of variables to nd the rst 5 lowest frequencies of free vibration. Reference: Edwards and Penney, Section 10.5....
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 Spring '08
 PHOENIX
 Frequency, Mode shape, Penney, Advanced Engineering Analysis, rigid spherical shell

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