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An oscillator is a positive feedback circuit which produces oscillations at its output. These oscillations may be sinusoidal or non-sinusoidal like square wave, triangular wave, spikes etc. :)

For more details search for "Barkhausens Criteria" for sustained oscillations in a positive feedback circuit and various oscillators like
1) Colpitts Oscillator
2) Hartley Oscillator
3) Wein Bridge Oscilaltor
4) Astabale Multivibrator
5) UJT Relaxation oscillator
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