-
In the system shown in the figure, r(t) = sin ωt
The steady-stat e response c(t) will exhibit a resonance peak at a frequency of_______ rad/sec
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- 2 √2
- √2
- 2
- None of these
Correct Option: A
| ∴ | = | = | |||||
| s(s + 4) | |||||||
| R(s) | 1 + | × 1 | 16 + s(s + 4) | ||||
| s(s + 4) | |||||||
| = | = | ||||
| R(jω) | 16 + jω(jω + 4) | 16 - ω² + 4jω |
| = | ∠ -tan-1 | |||
| √(16 - ω)² + (4ω)² | (16 - ω²) |
For resonance to occur
| √(16 - ω)² + (4ω)² = 0 | ||
| dω |
F(ω) = (16 - ω²)² + (4 ω)²
= ω4 + 256 - 32 ω² + 16ω²
= ω4 - 16 ω² + 256
| ∴ | = 4ω3 - 32 ω = 0 | |
| dω |
⇒ ω = √8 = 2 √2 rad / sec
