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A second order system with no zeros has its poles located at -3 + j4 and -3 – j4 in the s-plane. The undamped natural frequency and the damping ratio of the system are respectively.
1. 4 rad/s and 0.75
2. 3 rad/s and 0.60
3. 5 rad/s and 0.80
4. 5 rad/s and 0.60

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Best answer
Correct Answer - Option 4 : 5 rad/s and 0.60

Concept

The characteristic equation of a 2nd order system can be represented as follows:

\( {\rm{\Delta }}s=s^2+2\zeta \omega_n s+\omega_n^2\)

Analysis:

Pole locations = -3 + j4 and -3 - j4

The characteristic equation can be written as:

\( {\rm{\Delta }}s = \left\{ {s - \left( { - 3 + j4} \right)} \right\}\left\{ {s - \left( { - 3 - j4} \right)} \right\} \)

\(= {\left( {s + 3} \right)^2} + {4^2} = {s^2} + 6s + 25\)

\( \omega _n^2 = 25 \Rightarrow {\omega _n} = 5\;rad/s \)

\(2\zeta {\omega _n} = 6 \)

\(\zeta = 0.6 \)

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