For the system shown in the figure, with a damping ratio

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For the system shown in the figure, with a damping ratio ξ of 0.7. and undamped natural frequency ω_n of 4 rad / sec, the values of K and a are

1. K = 4, a = 0.35
2. K = 8, a = 0.455
3. K = 16, a = 0.225
4. K = 64, a = 0.9

Correct Option: C

M(s) =	G(s)	=	K / s ( + 2)
	1 + G(s) H(s)		1 + (1 + as) K / s (s + 2)

The characteristic equation is
s (s + 2) + K (1 + as) = 0
⇒ s² + s (2 + aK) + K = 0
Compare with equation s ² + 2 ξ ω_n s + ω_n² = 0, we get
K = ω_n ² = 4² = 16
∴ 2 ξ ω_n = (2 + aK)

⇒ a =	2 × 0.7 × 4 - 2	=	3.6	= 0.225
	16		16