Question

The damped natural frequency of an underdamped system is given by

• A. \(\omega_n\)
• B. \(\omega_n\zeta^2\)
• C. \(\omega_n\sqrt{1+\zeta^2}\)
• D. \(\omega_n\sqrt{1-\zeta^2}\)

Hint:

Important second-order system relations: \[ \omega_d=\omega_n\sqrt{1-\zeta^2} \] \[ T_p=\frac{\pi}{\omega_d} \] \[ M_p=e^{-\frac{\pi\zeta}{\sqrt{1-\zeta^2}}} \]

Answer 1

The Correct Option is D