= Solution
The <eigenvalues> of the recurrence <matrix> have <modulus> $e^{-\kappa T}<1$, so transients decay and the coefficients approach the fixed point
$$
x_\infty=(I-A)^{-1}b
=\frac{(g(T),1-f(T))^T}{[1-f(T)]^2+g(T)^2}.
$$
Thus
$$
|x_\infty|=\{[1-f(T)]^2+g(T)^2\}^{-1/2}.
$$
For $T=k\pi$ and $\kappa k\ll1$, this is
$$
|x_\infty|\sim\begin{cases}(\kappa k\pi)^{-1},&k\text{ even},\\[2mm]1/2,&k\text{ odd}.
\end{cases}
$$
Even multiples deliver impulses in phase and produce <resonance>; odd multiples alternate the phase and largely cancel.
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