Question

A second order system with a zero at –2 has its poles located at –3 + j4 and –3 – j4 in the s-plane. The undamped natural frequency and the damping factor of the system respectively are
1. 3 rad/s and 0.80
2. 5 rad/s and 0.80
3. 3 rad/s and 0.60
4. 5 rad/s and 0.60

Answer 1

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

According to the given information in the question, the transfer function can be found as:

\(T\left( s \right) = \frac{{s + 2}}{{\left( {s + 3 + j4} \right)\left( {s + 3 - j4} \right)}} = \frac{{G\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)

The characteristic equation is the roots of denominator of transfer function.

q(s) = 1 + G(s) H(s) ⇒ s² + 6s + 25          ---(I)

By comparing with standard equation

\({s^2} + 2\xi {\omega _n}s + \omega _n^2\)         ---(II)

By comparing both the equations

ω_n = 5 rad/sec

ξ = 0.6

Therefore, undamped natural frequency is 5 rad/sec

Damping ratio is 0.6.