# How to calculate Damping ratio and Damping frequency in matlab

### What is damping ratio?

The damping ratio is a parameter, usually denoted by ζ (zeta), that characterises the frequency response of a second order ordinary differential equation. It is specifically important in the study of control theory. It is also important in the harmonic oscillator.

The damping ratio provides a mathematical means to express the level of damping in a system relative to critical damping. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the system’s differential equation to the critical damping coefficient:

Damping ratio and damping frequency can be analysed in using matlab tool.

### System

Consider the system:

### Matlab code:

clc clear all close all num=[400]; dnum=[1 12 400] system=tf(num,dnum) omega=sqrt(dnum(3)) zeta=dnum(2)/(2*omega) step(system)

### Results:

#### Matlab file

Click here to download the matlab file.

If you want step by step guide for how to implement this code and view results please visit the youtube link: https://www.youtube.com/watch?v=SB2ydMtZxM8

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