A colleague asked me this question and I had no clue.
When a function (for instance, a sine wave) is multiplied by a decaying exponential, we call the phenomenon damping. What would it be called if the wave is multiplied by a growing exponential?
I suggested forcing or driving, since functions of that form arise in simple harmonic oscillators driven by sine waves with frequency equal to the oscillator's frequency. But I wondered if others had words for it.