Steady-state of a system and Fourier Transform

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I successfully found the Fourier Transform of a function $f(t)$. Suppose the Fourier transform looks like the one below, so its not easy to calculate the Inverse transform:

$$ F(w) = a ^{c - \sqrt{b -2\cdot i\cdot \omega}} $$

How do I obtain or analyze the "steady-state" of this system? Either $\frac{df}{dt}=0$ or $\lim_{t \to \infty} f(t) $?

Note that the FT that I wrote above is a simplified version of the one I am dealing with, and I have not been able to find the inverse FT of my function, so I prefer to analyze the steady-state using the Fourier transform, rather than reverting the transformation.