The dynamic equilibrium of a one-story building is described by the following equation: x(t) = xc(t) + X(t) where x(t) displacement in meters, t= time in seconds, xc(t) = e-04t[A cos t +B sin t], is the complementary function, and X(t) is the particular integral %3D (a) Determine the homogeneous second-order DE, assuming X (t) = 0.
The dynamic equilibrium of a one-story building is described by the following equation: x(t) = xc(t) + X(t) where x(t) displacement in meters, t= time in seconds, xc(t) = e-04t[A cos t +B sin t], is the complementary function, and X(t) is the particular integral %3D (a) Determine the homogeneous second-order DE, assuming X (t) = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The dynamic equilibrium of a one-story building is described by the following equation:
x(t) = xc(t) + X(t)
where x(t) displacement in meters, t= time in seconds,
xc(t) = e-04t[A cos t +B sin t], is the complementary function, and
X(t) is the particular integral
%3D
(a) Determine the homogeneous second-order DE, assuming X (t) = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F175104cb-e51e-4d8b-bca6-dfed5daee8af%2F51f75161-d52b-4a95-bc1c-53448ede06d2%2Fqan2czr.jpeg&w=3840&q=75)
Transcribed Image Text:The dynamic equilibrium of a one-story building is described by the following equation:
x(t) = xc(t) + X(t)
where x(t) displacement in meters, t= time in seconds,
xc(t) = e-04t[A cos t +B sin t], is the complementary function, and
X(t) is the particular integral
%3D
(a) Determine the homogeneous second-order DE, assuming X (t) = 0.
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