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.

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

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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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.

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