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Consider the 2-dimensional wave equation in polar coordinates utt displacement vibrations u (r, 0, t) of a circular membrane of radius R. Assume that the boundary is fixed. = c2V2u modeling the Use separation of variables to find all eigenfunctions, i.e., all solutions of the form u (r, 0, t) Q (r) (0) T (t). You only need to find the functions Q (r), O (0) and T (t). You do not need to put together to a series. You may assume that the constant " (0) 0 (0) is negative and also that the constant T" (t) /T (t) is also negative. This way you do not need to consider several cases.

Consider the 2-dimensional wave equation in polar coordinates utt displacement vibrations u (r, 0, t) of a circular membrane of radius R. Assume that the boundary is fixed. = c2V2u modeling the Use separation of variables to find all eigenfunctions, i.e., all solutions of the form u (r, 0, t) Q (r) (0) T (t). You only need to find the functions Q (r), O (0) and T (t). You do not need to put together to a series. You may assume that the constant " (0) 0 (0) is negative and also that the constant T" (t) /T (t) is also negative. This way you do not need to consider several cases.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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Consider the 2-dimensional wave equation in polar coordinates utt displacement vibrations u (r, 0, t) of a circular membrane of radius R. Assume that the boundary is fixed. = c2V2u modeling the Use separation of variables to find all eigenfunctions, i.e., all solutions of the form u (r, 0, t) Q (r) (0) T (t). You only need to find the functions Q (r), O (0) and T (t). You do not need to put together to a series. You may assume that the constant " (0) 0 (0) is negative and also that the constant T" (t) /T (t) is also negative. This way you do not need to consider several cases.
Transcribed Image Text:Consider the 2-dimensional wave equation in polar coordinates utt displacement vibrations u (r, 0, t) of a circular membrane of radius R. Assume that the boundary is fixed. = c2V2u modeling the Use separation of variables to find all eigenfunctions, i.e., all solutions of the form u (r, 0, t) Q (r) (0) T (t). You only need to find the functions Q (r), O (0) and T (t). You do not need to put together to a series. You may assume that the constant " (0) 0 (0) is negative and also that the constant T" (t) /T (t) is also negative. This way you do not need to consider several cases.
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