Question 9.6.1: Two Coupled RC Loops Draw the block diagram for the circuit ...

From equation (6) in Example 6.3.1

\frac{d v_{1}}{d t} = \frac{1}{RC} (v_{s}  −  2v_{1} + v_{o})
This gives
(RCs + 2)V_{1}(s) = V_{s}(s) + V_{o}(s)
or
V_{1}(s) = \frac{1}{RCs  +  2}  [V_{s}(s) + V_{o}(s)]           (1)
From equation (3) in Example 6.3.1
\frac{d v_{o}}{d t} = \frac{1}{RC} (v_{1}  −  v_{o})
This gives
(RCs + 1)V_{1}(s) = V_{1}(s)
or
V_{0}(s) = \frac{1}{RCs  +  1} V_{1}(s)         (2)
Equations (1) and (2) form the basis of the block diagram shown in Figure 9.6.8. The diagram can be reduced to find the transfer function, which is
\frac{V_{o}(s)}{V_{s}(s)} = \frac{1}{R^{2} C^{2} s^{2}  +  3RCs  +  1}