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:
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:
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The damping factor reduces the frequency of oscillation by a factor related to its magnitude As ζ increases the damped frequency decreases
Updated On: Jan 17, 2026
- 67.13 rad/sec
- 77.13 rad/sec
- 57.13 rad/sec
- 47.13 rad/sec
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The Correct Option is A
Solution and Explanation
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:
\( \omega_d = 80 \sqrt{1 - (0.7)^2} = 80 \times 0.714 \approx 67.13 \, \text{rad/sec} \)
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