2. Mechanical
A reciprocating or vibrating mechanical device like a piston or a tuning fork are both mechnical oscillators.
3. Mathematical
The mathematical description of an oscillator involves a description of a continuous function that varies cyclically above and below a mean or other reference, extending from infinity to +infinity, never fading, never diverging. This can be represented as a sequence:
For example the sequence 1, 1, 1, 1, 1, 1,... is an oscillation that is analogous to a squarewave generator. [This paragraph is horribly written; a mathematician who knows the conventions of this area could correct it. I have changed the incorrect word "series" to "sequence".]
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