Question

Solving for a forced oscillator:
we solve for an undriven damped oscillator to get the transient part,and solve for the steady state solution and add both to get the solution.

So how can the the sum of these
1. solution for undriven oscillator (for all time)
2. steady state sol for forced oscillator (valid for large times only)

give the behavior of forced oscillator (for all time).

the differential equation theory is okay but what's the physics behind it??

Answer 1

Suppose I shake you with certain frequency( our Fcos omega t). For the very first seconds you're shocked, you don't like it, so you involuntarily oppose that change. But I'm strong, I have force on you, and assuming that you are way weaker( you can't fight with me, you have no power source as I have) You start to accept your fate and your quick reaction(transient) dies out, but my will remains( steady state) The adding of those two solutions really lies at differential equation theory and I find it impossible to predict it( the answer for most difficult concepts is hidden in equations) If you want to be more quantitative watch this:
http://ocw.mit.edu/courses/physics/8-03-physics-iii-vibrations-and-waves-fall-2004/video-lectures/lecture-4/

Answer 2

i was watching this lecture series! i saw it till third and at the start of the 4th lecture i thought about this question. what you said is ,of course ,what happens and is said in the lectures.what i find weird is that the sum of a seemingly far off part(steady state solution) and the complete solution of a different situation(undriven oscillator) gives the answer to our much more complicated problem.

Answer 3

I told you the answer of physics problems are hidden in equations and we cannot intuitively
understand it. We know from differential equations that you have to add this zero solution to get full answer, and this is non intuitive.

Answer 4

yep.i guess that's it. these equations sure are non-intuitive...