The dynamic equilibrium of a one-story building is described by the following equation: u(t) = u.(t) + U(t) where u(t) = displacement in meters, t= time in seconds, uc(t) = e-0.25¢ [A cos 1.25t + B...

Extracted text: The dynamic equilibrium of a one-story building is described by the following equation: u(t) = u.(t) + U(t) where u(t) = displacement in meters, t= time in seconds, uc(t) = e-0.25¢ [A cos 1.25t + B sin 1.25t], is the complementary function, and U(t) is the particular integral (a) Determine the homogeneous second-order DE, assuming U(t) = 0. (b) Determine the non-homogeneous second-order DE, assuming U(t) = 1.6 t + 0.6. (c) Solve DE in (b) using Laplace Transform. (d) Determine the particular solution assuming u(0) = 0.6, and u(1) = 1. (e) Plot u vs t, then evaluate the solution in terms of shape, initial level, and final level.