How do you find the zero-input response in the frequency domain?

[Nat3]

I'm working on a problem and one part of it is finding the zero-input response of a system in the frequency (or "s") domain.

The zero-state response can be easily found in the frequency domain, it's just:

$Y_{zs} = X(S)H(S)$

But I can't for the life of me find the equation for calculating the zero-input response. I've been looking through my textbook and online and simply can't find anything.. How is it done?

 

[Nat3]

Well, after considerable effort I finally figured it out. Zero-input means you set the input to zero :-)

Actually, there was more to it than that. You have to include initial conditions in the equation or it won't work, and that was the part that was tripping me up.

Case closed!