The classic example of resonance is pushing someone on a swing. If the pushes occur at the systems natural frequency, the swing progressively goes higher. The farther the frequency of pushes from is the natural frequency, the more the pushes will "interfere" with the motion of the swing which produces less amplitude.
It occurred to me, that taking the convolution of a systems natural mode and an input frequency, for complex $m,n$
$$\int_0^te^{n(t-x)}e^{mx}dx$$
$$=e^{nt}\int_0^te^{-nx}e^{mx}dx$$
For all $m\ne n$
$$=\frac{e^{mt}-e^{nt}}{m-n}$$
and for $m=n$ we get the classic resonant solution
$$te^{nt}$$
Do systems only resonante at their characteristic modes due to orthoginality with sinusoids of other frequencies?