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The frequency response of G(s) = 1 plotted in the complex G(jω) [s(s + 1)(s + 2)]
plane (for 0 < ω < ∞) is
Correct Option: A
| G(s) = | ||
| s(s + 1)(s + 2) |
| G(jω) = | ||
| jω(jω + 1)(jω + 2) |
| M = | ||
| ω√ω² + 1 √ω² + 4 |
| ∠ φ = -90 - tan-1ω - tan-1 | ||
| 2 |

For ω = 0, M = ∞ ; ∠ φ = – 90
For ω = ∞, M = 0; ∠ φ = – 90 – 90 – 90 = – 270
So Cutting Real Axis
Imaginary part of G(jω) = 0
i.e. Img {G(jω)} = 0
| ⇒ Im | ![]() | ![]() | = 0 | |
| jω(-ω2 + 3)ω + 2 |
| ⇒ Im | ![]() | ![]() | = 0 | |
| -jω3 - 3ω2 + 2jω |
| ⇒ Im | ![]() | ![]() | = 0 | |
| - 3ω2 + j(2ω - ω3) |
| ⇒ Im | ![]() | ![]() | = 0 | |
| (3ω2)2 + (2ω - ω3)2 |
∴ 2ω – ω3 = 0
⇒ ω2 = 2 . ω = 0
Neglecting ω = 0, we have
ω = √2
| ∴ M |at ω = √2 = | = | ⇒ | < | ![]() | 3 | ![]() | |||
| √2 √3 √2 + 4 | √36 | 6 | 4 |







