Question

The undamped natural frequency of system is 80 rad/sec. A damper is provided in the system having damping factor 0.7. The damped natural frequency of the system in rad/sec will be:

• A. 67.13 rad/sec
• B. 77.13 rad/sec
• C. 57.13 rad/sec
• D. 47.13 rad/sec

Hint:

The damping factor reduces the frequency of oscillation by a factor related to its magnitude As ζ increases the damped frequency decreases

Answer 1

The Correct Option is A

The damped natural frequency \( \omega_d \) is related to the undamped natural frequency \( \omega_n \) and the damping factor \( \zeta \) by the following formula:

\( \omega_d = \omega_n \sqrt{1 - \zeta^2} \)

Given that \( \omega_n = 80 \, \text{rad/sec} \) and \( \zeta = 0.7 \), we can calculate the damped natural frequency as:

\( \omega_d = 80 \sqrt{1 - (0.7)^2} = 80 \times 0.714 \approx 67.13 \, \text{rad/sec} \)