How sinusoidal oscillators produce sinusoids?

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A linear oscillator produces sinusoidal output due to its second-order system characteristics, which inherently respond to inputs with sinusoidal waveforms. The oscillator operates with a gain slightly above unity and incorporates small non-linearities to stabilize the output amplitude. This stabilization prevents the amplitude from increasing indefinitely, resulting in a consistent sinusoidal signal. The characteristic equation and circuit poles play a crucial role in defining the oscillator's behavior. Overall, the combination of these factors explains why sinusoidal signals emerge from what might begin as random noise.
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Why/How does a linear oscillator give >>>sinusoidal<<< output?

I am basically confused how the sinusoidal signal output generates from a random noise? Why sinusoidal and not something else?

Can this be explained from the characteristic equation/circuit poles?
 
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sns said:
Why/How does a linear oscillator give >>>sinusoidal<<< output?

I am basically confused how the sinusoidal signal output generates from a random noise? Why sinusoidal and not something else?

Can this be explained from the characteristic equation/circuit poles?
An oscillator is a second order system, an amplifier with a gain fractionally over 1 and a tiny bit of non-linearity to drop the gain at the peaks to 0.999. The natural response of a critically damped second order system to a step or impulse is the sinusoid. With a loop gain of just over unity, it would be a sinusoid of ever-increasing amplitude, but tiny non-linearities are incorporated to level it out at an amplitude appropriate to the circuit parameters.
 
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