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# Consider a circular membrane r = a. For noncircularly symmetric eigenfunctions (m = 0) ISBN: 9780321797056 284

## Solution for problem 9.6.9 Chapter 9.6

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 9.6.9

Consider a circular membrane r = a. For noncircularly symmetric eigenfunctions (m = 0), (9.6.18) is valid with 0 = c1(1) 0 + c2(2) 0 , where (1) 0 and (2) 0 are two mutually orthogonal eigenfunctions corresponding to the same eigenvalue 0. Here, c1 and c2 are arbitrary constants. (a) Determine a homogeneous linear system of equations for c1 and c2 derived from the fact that 1 has two homogeneous solutions (1) 0 and (2) 0 . This will be the compatibility condition for (9.6.18) with (9.6.19). (b) Solve the linear system of part (a) to determine the perturbed frequencies and the corresponding natural modes of vibration.

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Limits of Infinity: In this section we are going to explore limits that go towards infinity. Limits of infinity imply, that we are going to be looking at what impacts a function if you were to let x get very large in either the positive or negative sense. Also, as we’ll soon see, these limits may also create infinity as a value. It...

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##### ISBN: 9780321797056

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