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This is question about a term whose definition I can find anywhere. I am given to solve a differential equation and one of the questions asks to show that the solution (we are given initial data) is purely oscillatory as something becomes large. Then we are asked to find the amplitude. Would anyone be kind enough to provide me with the definitions of purely oscillatory and amplitude in this context?

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"Purely oscillatory" typically refers to a lack of damping, meaning that the spring does not lose amplitude as it oscillates. This means that there is no first derivative term in the diff eq defining the oscillatory motion.

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a) You've used one of the terms that was supposed to be defined, "amplitude". b) The second sentence is correct in the context of ordinary second-order linear differential equations with constant coefficients, which may or may not be the subject of the question. –  joriki Feb 5 '13 at 0:17
This is the case for (b). I still do not understand (a). –  user44069 Feb 5 '13 at 0:21
@Stefan: The amplitude is the maximal displacement, i.e. the coefficient in front of the sinusoidal term; that is, if the solution is $A\cos(\omega t+\phi)$, the amplitude is $A$. –  joriki Feb 5 '13 at 0:24
@joriki: given what the OP was saying, I felt I could safely assume that we were talking about constant coefficient DE's, 2nd order. As for amplitude, yes, I missed that and thanks for filling in that gap. –  Ron Gordon Feb 5 '13 at 0:39
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