Question

A second order system is designed such that, damping ratio should vary between 0.25 to 0.5 and natrual frequency should vary from 2 rad/sec to 4 rad/sec, then roots lie on

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Damping ratio, $\xi =\cos \theta$

For $\xi =0.25$

$\theta ={\cos }^{-1}\left(0.25\right)=75.52{}^{\circ }$

$\xi =0.5$

$\theta ={\cos }^{-1}\left(0.5\right)=60{}^{\circ }$

and ${\omega }_n$ varies from 2 rad/sec to 4 rad/sec.

the plot can be shown as: