Question 9.17: Find the transform F(s) from the pole-zero diagram of Figure......

This diagram has four poles and four zeros, two of which are at infinity. Starting with the poles we see that two are complex conjugates at s₁, s₂ = −100 ± j100, and there are two at s = 0.

F(s) = \frac{K(zeros)}{s^{2}(s  +  100  −  j100)(s  +  100  +  j100)}

Including the zeros and the specified K value, we get

F(s) = \frac{10^{6}(s  +  100)(s  −  100)}{s^{2}(s  +  100  −  j100)(s  +  100  +  j100)} = \frac{10^{6}(s^{2}  –  10^{4})}{s^{2} (s^{2}  +  200s  +  2  ×  10^{4})}