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Differential Equations by Pearson
book

Differential Equations by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
472 pages
13h 25m
English
Pearson India
Content preview from Differential Equations by Pearson
8-78 Diff erential Equations
The solution for the initial displacement given by (8.457) and zero
initial velocity is
1
2
1
(2 1) (2 1)
(1)
4
(,) sin cos
(2 1)
m
m
mx mat
yxt
ml l
=
−−
=
pp
p
(8.461)
8.13.7 Vibrating String with Given Initial Velocity and
Zero Initial Displacement
Next, we consider the case when the string is released from its horizon-
tal position with zero initial displacement but with an initial velocity
given at x by g ( x). The boundary value problem for the displacement
function is
22
2
22
for 0 , 0
yy
axlt
tx
∂∂
=≤≤>
∂∂
(8.462)
(0,) 0 (,) for 0yt
ylt t== >
(8.463), (8.464)
zero initial
displacement:
(,0) 0
for 0
(,0) ()
yx
xl
y
xgx
t
=
≤≤
=
prescribed ...
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Publisher Resources

ISBN: 9781299487406Publisher Website