Exercise 9.13 An harmonic oscillator?

(a)

(b)

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

(c)

An answer:

(d)

An answer:
No, the only solutions for $\angle A_{\mathit{loop}}(\mathit{j\omega })$ is for zero or infinite frequencies. Neither of these is considered to be a valid oscillation frequency.

(e)

An answer:
Yes, harmonic oscillation is possible. A derivation using symmetry is the easiest, but plain mathematical solvinf is only a little more work. Both lead to ${\omega }_{\mathit{osc}}=1∕\mathit{RC}$ and $A_{\mathit{buf}}=-4$.