Describing functions method

$$\frac{Y\left( s\right) }{R\left( s\right) } = \frac{N.G\left( s\right) }{1+N.G\left( s\right) }\\$$ (2.1)

if

$$1+N.G(s) = 0$$ (2.2)

$$\Rightarrow G(s) = \frac{-1}{N}$$ (2.3)

$$\Rightarrow \vert G(j \omega)\vert = \frac{1}{N}$$ (2.4)

it is a pole. If $x= A\sin \omega t$

$$Y( A\sin \omega t,\omega A\sin \omega t) = \sum A\left( A,\omega \right)\left( \sin n\omega t+\phi \left( A,\omega \right) \right)$$ (2.5)

approximating the non-linearity N by a function of above type but only the first frequency:

$$N = \frac{\left( A,\omega \right) }{A}e^{j\phi \left( A,\omega \right) }$$ (2.6)

This implies non-linearity is substituted by a describing function.