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Basics of Signal Flow Graph

In the system...

Question

In the system whose signal flow graph is shown in figure. $U_{1} (s)$ and $U_{2} (s)$ are inputs. the transfer function $Y (s) / U_{1} (s)$ is

\frac{k_{1}}{J L s^{2} + J R s + k_{1} k_{2}}

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\frac{k_{1}}{J L s^{2} - J R s - k_{1} k_{2}}

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\frac{k_{1} - U_{2} (R + S L)}{J L s^{2} + (J R - U_{2} L) s + k_{1} k_{2} - U_{2} R}

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\frac{k_{1} - U_{2} (S L + R)}{J L s^{2} - (J R - U_{2} L) s - k_{1} k_{2} + U_{2} R}

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Solution

The correct option is A $\frac{k_{1}}{J L s^{2} + J R s + k_{1} k_{2}}$
Transfer function,
$\frac{Y (s)}{U_{1} (s)} = \frac{\frac{K_{1}}{L J s^{2}} [1]}{1 - [- \frac{R}{L S} - \frac{K_{1} K_{2}}{L J s^{2}}]}$

$= \frac{K_{1}}{L J s^{2} + R J s + K_{1} K_{2}}$

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