Question

A second order control system has a damping ratio as 0.6 and natural frequency of oscillations as 11 rad/sec. What will be the Damped frequency of oscillation?
1. 2.6 rad/sec
2. 8.8 rad/sec
3. 6.9 rad/sec
4. 5.6 rad/sec

Answer 1

Correct Answer - Option 2 : 8.8 rad/sec

Concept:

Damped natural frequency of a second order system is given by

\({ω _d} = {ω _n}\sqrt {1 - {\xi ^2}} \)

Where,

ωn = Natural frequency

ζ = Damping ratio

Calculation:

Given-

ωn = 11 rad/sec

ζ = 0.6

Now, natural damped frequency can be calculated as

\({ω _d} = {11}\sqrt {1 - {(0.6)^2}} \)

ωd = 11 x 0.8

ωd = 8.8 rad/sec