In the system whose signal flow graph is shown in figure. \(U_1(s)\) and \(U_2(s)\) are inputs. The transfer function \(\frac{Y(s)}{U_1(s)}\) is
1. \( \frac{k_1}{JLs^2 + JRs + k_1 k_2}\)
2. \( \frac{k_1}{JLs^2 - JRs - k_1 k_2}\)
3. \( \frac{k_1 - U_2(R + sL)}{JLs^2 + (JR -U_2L)s + k_1 k_2 - U_2R}\)
4. \( \frac{k_1 - U_2(R - sL)}{JLs^2 - (JR -U_2L)s - k_1 k_2 + U_2R}\)
I have a doubt that whether the input \(U_2\) will come in the transfer function or not? I'm confused between option (1) and (3).
1. \( \frac{k_1}{JLs^2 + JRs + k_1 k_2}\)
2. \( \frac{k_1}{JLs^2 - JRs - k_1 k_2}\)
3. \( \frac{k_1 - U_2(R + sL)}{JLs^2 + (JR -U_2L)s + k_1 k_2 - U_2R}\)
4. \( \frac{k_1 - U_2(R - sL)}{JLs^2 - (JR -U_2L)s - k_1 k_2 + U_2R}\)
I have a doubt that whether the input \(U_2\) will come in the transfer function or not? I'm confused between option (1) and (3).