Exercise 9.18 An harmonic oscillator and Nyquist plots

Given is the circuit below. This circuit is intended to be a harmonic oscillator. The voltage gain of the voltage buffer at the top of the schematic is a positive real valued factor $A_{\mathit{buf}}$. The value of all resistors is the same (R), and that the capacitors have identical values (C).

(a)

Which condition(s) must be satisfied to get harmonic oscillation?

(b)

Which one of the following Nyquist plots corresponds to the open loop transfer function $A_{\mathit{loop}}(\mathit{j\omega })$ of the circuit above? You may assume $A_{\mathit{buf}}>0$ here.

(c)

Can this circuit oscillate harmonically for a $A_{\mathit{buf}}>0$? If so, at what frequency?

(d)

Can this circuit oscillate harmonically for a $A_{\mathit{buf}}<0$? If so, at what frequency?