# Matlab: transfer function determination

1. Sep 1, 2010

### serbring

I have a 2 dof vibration system, I have determined the differential equation of the model, can I determine the trasfer function readily with matlab, without using manual algebra operation?
In other word, I have that differential equation system:

[m]x''+[c]x'+[k]x=[f]

where:
[m] mass matrix
[c] damping matrix
[k] stiffness matrix
[f] external forces matrix

through laplace transformation I obtain:

s^[m]x(s)+s[c]x(x)+[k]x(s)=[f]

where s is the laplace variable, how can I find [f]/[x]?
I'm searching a way for estimating readily the transfer function of mechanical system, it is a loss of time to perform the calculation every time

2. Sep 7, 2010

### serbring

may anyone help me?

3. Sep 7, 2010

### ddarvil

You've pretty much got the TF. Rearrange the laplace you've done above so you get f/x = tf (factorise the left side wrt to X). From there, you can use matlab to analyse the TF.
MATLAB tools(look in help): tf, bode, ltview.
The time required to manually calculate the TF is trivial for systems like this. You can use dsolve to get a symbolic solution to the ODE but it's not really necessary

4. Oct 4, 2010

### serbring

I know the tf, bode function, but how can I use them when the system has more than one dofs?