Hi, I have been working on the solution to a damped, sinusoidally driven system and their electric-circuit analogs. I can break the equation of motion into the homogeneous and particular portions, and understand that x(t) is the sum of the two solutions. I also understand that the homogeneous solution is the rate of decay and that the particular solution is the steady state portion. However, I can't resolve why the homogeneouos portion can be totally ignored when calculating motion or even the current. Even though it is decaying, isn't that part of the solution part of the reality of the system in question? I am looking at Marion and Thornton "Classical Dynamics," 4th edition, sections 3.6 - 3.8. I hope my question makes sense. I appreciate any input anyone can provide.