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  1. For the system shown in figure, with a damping ratio ξ for 0.7 and an undamped natural frequency ωn of 4 rad/sec, the value 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

From figure
table>G(s) = C(s) =

G(s)
R(s)1 + G(s)H(s)
K/s(s+2)
1 + (1 + as) K/s (s+2)

The characteristic equation on comparing equation with the standard equation



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