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...

Extracted 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.