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?

"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.