The vertical displacement u of a circular membrane of radius 1, fixed at the boundary, satisfies the partial differential equation = V?u with u(1,8,t) = 0. Find the displacement u of a vibrating circular membrane subject to the initial conditions u(r,e,0) = -5/,(z3r) + 4/0(Z6r), ди ar (r, 8,0) = 0. Here, z, denotes nth root of the 0th order Bessel function of the 1st kind.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The vertical displacement u of a circular membrane of radius 1, fixed at the boundary, satisfies the
partial differential equation
with
u(1,8, t) = 0.
Find the displacement u of a vibrating circular membrane subject to the initial conditions
u(r,e,0) = -5/,(z3r) + 4/,(z,r),
ди
(r,0,0) = 0.
at
Here, z, denotes nth root of the Oth order Bessel function of the 1st kind.
Transcribed Image Text:The vertical displacement u of a circular membrane of radius 1, fixed at the boundary, satisfies the partial differential equation with u(1,8, t) = 0. Find the displacement u of a vibrating circular membrane subject to the initial conditions u(r,e,0) = -5/,(z3r) + 4/,(z,r), ди (r,0,0) = 0. at Here, z, denotes nth root of the Oth order Bessel function of the 1st kind.
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