When studying Calculus, I asked this question about why non-repeated and repeated factors are handled differently in partial fraction decomposition. As I work Laplace Transform problems, I'm noticing repeated factors occur when there is resonance between an ODE's forcing term and associated homogeneous solution. This makes at least half of a bit of sense, since the algebraic step of a Laplace Transform problem involves dividing everything by the characteristic polynomial, which is related to the associated homogeneous solution. Perhaps the denominator of a forcing term's Laplace Transform is related to the homogeneous linear ODE which that forcing term would solve, creating this overlap in the resonant case.
Is it accurate to say that repeated factors in the s-domain occur if, only if, or if and only if the ODE has resonance? If so, is my linked question about the additional term in a repeated-factor partial fraction decomposition nothing more than the s-domain framing of the common question of why an additional factor of $t$ appears in the particular solution to a resonant linear ODE?