# Finding Damped Frequency of a State Space Matrix Equation with MATLAB

• MATLAB
• feicobain
In summary, the individual is seeking assistance with calculating the damped frequency of a state space matrix equation in the context of a vibration problem involving a tyre mechanic issue. They have derived the state space equation and have identified the matrices [A] and [B], but do not know how to calculate the damped frequency. They are aware that the mass, stiffness, and damping ratio are needed to calculate it and have tried searching for information on damped natural frequency. They also mention the possibility of having a second order system and the need to derive the transfer function.

#### feicobain

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 don't 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

KLoux said:
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 couldn't 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

## 1. What is a damped frequency in a state space matrix equation?

A damped frequency refers to the rate at which the amplitude of a system's response decreases over time due to the presence of damping.

## 2. How is the damped frequency calculated in a state space matrix equation?

The damped frequency can be calculated by finding the complex conjugate poles of the system's transfer function and taking the imaginary part of these poles.

## 3. What is the significance of finding the damped frequency in a state space matrix equation?

Finding the damped frequency allows us to understand the behavior of a system and its response to different inputs. It also helps in designing control systems for the system.

## 4. How can MATLAB be used to find the damped frequency of a state space matrix equation?

MATLAB has built-in functions and tools that can be used to analyze the state space representation of a system and calculate its damped frequency. These include the 'damp' and 'eig' functions.

## 5. Are there any limitations to using MATLAB for finding the damped frequency of a state space matrix equation?

While MATLAB can provide accurate results for finding the damped frequency, it is important to note that the accuracy of the results depends on the accuracy of the system's model and the assumptions made in the analysis.