Find the equivalent transfer function, T(s) = C(s) / R(s), for the system shown in figure using Maso's Rule and block di...

$$\begin{gathered} Here, \\ Forward path gain \\ Path 1 -> \frac{1}{s^2}x\frac{50}{s+1}x s \\ Path 2 -> \frac{1}{s^2}x\frac{50}{s+1}x 2 \\ Individual loop gain \\ Loop 1 -> \frac{1}{s^2}x\frac{50}{s+1}x s x (-1) \\ Loop 2 -> \frac{50}{s+1}x \frac{2}{s} x (-1) \end{gathered}$$

$$\begin{gathered} According to mason\text{'}s gain formula \\ \frac{C\left(s\right)}{R\left(s\right)} = \frac{Path 1 + Path 2 }{1- Loop1 - Loop2} \\ = \frac{\left(\frac{1}{s^2}x\frac{50}{s+1}x s \right)+\left( \frac{1}{s^2}x\frac{50}{s+1}x 2 \right)}{1- \left(\frac{1}{s^2}x\frac{50}{s+1}x s x (-1)\right) -\left( \frac{50}{s+1}x \frac{2}{s} x (-1)\right)} \\ \mathbf{ }\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{50}\mathbf{s}\mathbf{+}\mathbf{100}}{{\mathbf{s}}^{\mathbf{3}}\mathbf{+}{\mathbf{s}}^{\mathbf{2}}\mathbf{+}\mathbf{50}\mathbf{s}\mathbf{+}\mathbf{100}} \end{gathered}$$