How sinusoidal oscillators produce sinusoids?

[sns]

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?

 

[Bob S]

The standard sinusoidal oscillator is the Wein Bridge. See http://www.ti.com/lit/an/sloa060/sloa060.pdf

 

[NascentOxygen]

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.