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Greeley [361]
3 years ago
15

What is the damped natural frequency (in rad/s) of a second order system whose undamped natural frequency is 25 rad/s and has a

damping ratio of 0.3?
Engineering
1 answer:
TiliK225 [7]3 years ago
3 0

Answer:

damped natural frequency = 23.84 rad/s

Explanation:

given data

damping ratio = 0.3

undamped natural frequency = 25 rad/s

to find out

damped natural frequency of a second order system

solution

we know that if damping ratio is = 0

then it is undamped system

and if damping ratio is > 1

then it is overdamped system

and  and if damping ratio is ≈ 1

then it is critical damped system

so damped natural frequency of a second order system formula is

damped natural frequency = wn × \sqrt{1-r^2}

here wn is undamped natural frequency and r is damping ratio

damped natural frequency = 25 × \sqrt{1-0.3^2}

damped natural frequency = 23.84 rad/s

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Answer:

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Substituting,

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