# Matlab, how to find damped frequency of a first order sate space matrix euqation?

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## Main Question or Discussion Point

Matlab, how to find damped frequency of a sate space matrix euqation?

Hello:

I am working on a tyre mechanic problem basically it just a vibration problem so far I have dervied the the state space equation which is in the form

x'=[A]x+u

[A] is 2x2 matrix, is a 1X2 matrix (u could be treated as 0) and they are both known

but I dont know how to calculate the damped frequency. Anybody could help please?

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How did you define your states? If you know (or can extract from your A matrix, based on how you defined your states) your mass, stiffness, and damping ratio you can calculate it using some basic vibration equations. Try googling "damped natural frequency." The wikipedia article shows how to calculate it based on the undamped natural frequency and damping ratio.

-Kerry

By the way - it sounds like you've probably got a second order system

By the way - it sounds like you've probably got a second order system
Ya you are right it is a second order. Thanks dude. I know that if I have the mass, stffness and damping matrix can work out the natural frequncy and damping ratio so it is the damped frequency but the problem is I couldnt extract the M,K,C matrix from [A]. I have seen the damp function in matlab. I think what I need to do it is to derive the transfer function of the state space equation.

If you can derive the transfer function yourself, that should give you what you need. Be aware that there can be multiple state-space representations for the same system depending on how you construct your state vector.

-Kerry