This is a Colpitts oscillator, an oscillator that uses an LC circuit combined with a transistor for feedback.
With the transistor removed, the inductor and two capacitors form a resonant circuit, like the LRC example. Current moves back and forth as the capacitors charge and discharge through the inductor. The transistor amplifies this oscillation and prevents it from dying out.
The transistor cannot conduct until C1 is charged to about 680mV. When the transistor is off, the output is around 4.5 V. Current from the 1k resistor and the inductor charges C2. The current through the inductor slows and then reverses, charging C1 again. When it is charged, the transistor conducts, bringing the output low. As the oscillation continues, the transistor turns off again. Current through the 1k resistor keeps the oscillation going.
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