Exercise 9.2 An LC oscillator

Consider the harmonic oscillator circuit shown below. The amplifier in this circuit schematic has a finite gain A.

a)

Derive an expression for the transfer function of the feedback network, i.e. from the output $v_{\mathit{out}}$ to the differential input voltage $v_{+}-v_{-}$ of the amplifier.

b)

For which $\omega$ is the derived signal transfer real?

c)

Derive an expression for the amplifier gain A that is needed for harmonic oscillation.