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The unit step response of a second order linear system with zero initial states is given by
C (t) = 1 + 1.25 exp (– 6t) sin (8t – tan–1 1.333); t ≥ 0
The damping ratio and the undamped natural frequency of oscillation for the system are respectively—
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- 0.6 and 10 rad/s
- 0.6 and 12.5 rad/s
- 0.8 and 10 rad/s
- 0.8 and 12.5 rad/s
- 0.6 and 10 rad/s
Correct Option: A
From the expression for C (t), we get
8 = ωn√1 – ξ2 …(i)
and
√1 – ξ2/ξ = 1.333 …(ii)
solving these two equation, we get
ωn = 10 rad/sec, and ξ = 0.6
