# Definition of purely oscillatory

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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@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