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 cos t + 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. (d) Use Laplace Transform to solve the same DE with same initial conditions. Compare it with the solution from (c). (e) Plot x vs t, then evaluate the particular solution in terms of shape, initial level, and final level.
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 cos t + 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. (d) Use Laplace Transform to solve the same DE with same initial conditions. Compare it with the solution from (c). (e) Plot x vs t, then evaluate the particular solution in terms of shape, initial level, and final level.
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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please part d and e ,, i could not find the answers
![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 cos t + 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.
(d) Use Laplace Transform to solve the same DE with same initial conditions. Compare it
with the solution from (c).
(e) Plot x vs t, then evaluate the particular solution in terms of shape, initial level, and final
level.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F537dc467-2015-41a7-beee-d23bb0e89ca1%2F0b2e1b21-33dd-4ef1-8327-ec8530f5c629%2Fgirertd.png&w=3840&q=75)
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 cos t + 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.
(d) Use Laplace Transform to solve the same DE with same initial conditions. Compare it
with the solution from (c).
(e) Plot x vs t, then evaluate the particular solution in terms of shape, initial level, and final
level.
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