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The unity feedback system is characterised by an open loop transfer function G(s) = K/s(s + 10). Determine the gain K, so that the system will have damping ratio of 0.5.
1. 10
2. 100
3. 1000
4. 0.1

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Correct Answer - Option 2 : 100

G(s) = K/s(s + 10)

Characteristic equation: 1 + G(s)H(s) = 0

⇒ s (s + 10) + K = 0

⇒ s2 + 10s + K = 0

⇒ ωn = √k

⇒ 2ζ (√k) = 10

⇒ 2 × 0.5 × (√k) = 10

⇒ K = 100

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