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Two necessary conditions for oscillatory behavior of physical systems

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There are at least two ways to describe the necessary conditions for oscillatory system behavior. Explain two of them.

My thoughts: I've heard of using displacement as the variable and using angular movement as the variable, but I am having a hard time confirming this/visualizing this theory. Would someone be able to confirm the validity and provide proof/explanation of these assumptions? If assumptions are wrong, what are the necessary conditions for oscillatory system behavior?

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Solution Summary

We give two necessary conditions for a physical system to have in order for it to undergo oscillatory behavior.

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In order for a system to undergo oscillatory behavior, it must have an equilibrium state. The system will then undergo oscillatory behavior if it is displaced from equilibrium by a ...

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