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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.

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    $\begingroup$ "Negative damping" or "positive feedback" are common. $\endgroup$ Apr 27, 2011 at 17:13
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    $\begingroup$ Driven/driving is certainly the term I've heard; see here for example. $\endgroup$ Apr 27, 2011 at 17:15
  • $\begingroup$ Another possibility is "resonance". But in general the terminology would depends on "what caused the exponential growing mode" in the first place. It may be that your friend is Merlin in disguise. $\endgroup$ Apr 27, 2011 at 19:08
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    $\begingroup$ People (at least in electrical engineering) use amplification (=gain) as the opposite of damping (=loss)... $\endgroup$
    – Fabian
    Apr 27, 2011 at 20:13
  • $\begingroup$ Driven is fine, but depending on the situation "resonance disaster" comes to mind, too. $\endgroup$
    – Phira
    Apr 28, 2011 at 0:15

3 Answers 3

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I would call reinforcing and amplifying a signal positive feedback, and where you have neither dampening nor feedback I would call that resonance or ringing.

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In physics, it is indeed called forcing or driving. For example, the solutions to a spring problem satisfy the spring equation (the solutions are sines). If you apply an external force to the object attached to the spring, depending on the nature of the force, it can have a driving effect on the object. If you for example apply a sinusoidal, periodic force with the same frequency as the characteristic frequency of the spring system, you shall see that the solution will grow in magnitude for increasing $t$.

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    $\begingroup$ I disagree. In the typical spring-mass-damper, $m\ddot{x} + c\dot{x}+kx = F(x,t)$, the "forcing" term is $F(x,t)$, but the damping coefficient term is $c$. Changing signs on $c$ such that the damping effect is reversed is not the same as adding a forcing function. $\endgroup$
    – Emily
    Aug 11, 2014 at 16:05
  • $\begingroup$ You are right, I was trying to explain it in physical terms and in mechanical systems negative damping does not exist so you have to resort to some sort of external driving force. If you managed to apply a driving force $F(x,t) = k \dot{x}$ $k > c$ then the effective damping would be negative but I am not sure if you can realize that. $\endgroup$ Aug 11, 2014 at 16:24
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isn't "amplification" more appropriate?

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