Exercise 9.12 An harmonic oscillator?

(a)

(b)

An answer:
The combined voltage transfers of the four stages is $A_{\mathit{loop}}(\mathit{j\omega })=\frac{A_{\mathit{buf}}}{{(1+\mathit{j\omega RC})}^4}$

(c)

An answer:

(d)

An answer:
To get $\angle A_{\mathit{loop}}=N\cdot 360^{\circ }$ with a positive $A_{\mathit{buf}}$ two solutions follow:

$\omega =0$
$\omega \to \infty$
These are not considered as valid frequencies for an harmonic oscillator. Hence: no.

(e)

An answer:
To get $\angle A_{\mathit{loop}}=N\cdot 360^{\circ }$ with a negative $A_{\mathit{buf}}$ one solution follows:

$\angle A_{\mathit{loop}}(j{\omega }_{\mathit{osc}})=N\cdot 360^{\circ }$
$\angle \frac{1}{1+\mathit{j\omega RC}}=-45^{\circ }$
this leads to ${\omega }_{\mathit{osc}}=1∕\mathit{RC}$ and $A_{\mathit{buf}}=-4$.