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A circular membrane of unit radius fixed along its boundary starts vibrating from rest nd has initial deflection ufr, 0) = f(r). Show that the deflection ufr, t) of the membrane at any instant is given by frf(r) Jo(ar) dr, 2 u(r, t) = Ž Am cos (camt). J.(ar) where A… ² J(am) m = 1 and a (m = 1, 2, ...) are the positive roots of the Bessel function Jolk) = 0.

A circular membrane of unit radius fixed along its boundary starts vibrating from rest nd has initial deflection ufr, 0) = f(r). Show that the deflection ufr, t) of the membrane at any instant is given by frf(r) Jo(ar) dr, 2 u(r, t) = Ž Am cos (camt). J.(ar) where A… ² J(am) m = 1 and a (m = 1, 2, ...) are the positive roots of the Bessel function Jolk) = 0.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
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A circular membrane of unit radius fixed along its boundary starts vibrating from rest and has initial deflection ufr, 0) = f(r). Show that the deflection u(r, t) of the membrane at any instant is given by [₁rf(r)Jo(ar) dr, u(r, t) = Ž Am cos (cœ„t). J₂(α„r) where A„ = 0 m = 1 and a(m = 1, 2, ...) are the positive roots of the Bessel function J,(k) = 0. 2 J(am) Jo
Transcribed Image Text:A circular membrane of unit radius fixed along its boundary starts vibrating from rest and has initial deflection ufr, 0) = f(r). Show that the deflection u(r, t) of the membrane at any instant is given by [₁rf(r)Jo(ar) dr, u(r, t) = Ž Am cos (cœ„t). J₂(α„r) where A„ = 0 m = 1 and a(m = 1, 2, ...) are the positive roots of the Bessel function J,(k) = 0. 2 J(am) Jo
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