The dynamic equilibrium of a one-story building is described by the following equation: x(t) = x.(t) + X(t) where x(t) = displacement in meters, t= time in seconds, x.(t) = e-0.4[A cost + B sin t], is the complementary function, and X(t) is the particular integral (a) Determine the homogeneous second-order DE, assuming X(t) = 0. (b) Determine the non-homogeneous second-order DE, assuming X(t) = 10. (c) Determine the particular solution of the DE in (b) assuming x(0) = 0, and x'(0) = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The dynamic equilibrium of a one-story building is described by the following equation:
x(t) = x.(t) + X(t)
where x(t) = displacement in meters, t= time in seconds,
x.(t) = e-0.4[A cost + B sin t], is the complementary function, and
X(t) is the particular integral
(a) Determine the homogeneous second-order DE, assuming X(t) = 0.
(b) Determine the non-homogeneous second-order DE, assuming X(t) = 10.
(c) Determine the particular solution of the DE in (b) assuming x(0) = 0, and x'(0) = 0.
Transcribed Image Text:The dynamic equilibrium of a one-story building is described by the following equation: x(t) = x.(t) + X(t) where x(t) = displacement in meters, t= time in seconds, x.(t) = e-0.4[A cost + B sin t], is the complementary function, and X(t) is the particular integral (a) Determine the homogeneous second-order DE, assuming X(t) = 0. (b) Determine the non-homogeneous second-order DE, assuming X(t) = 10. (c) Determine the particular solution of the DE in (b) assuming x(0) = 0, and x'(0) = 0.
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