# A 2nd Order ODE

amir99civil
Dear All,

I have a Problem about a 2nd order ode. I don't know how it can be solved with Matlab. If someone know about it then please let me know. I need to get the values of x & y. All other values are known.

The equation is:

[ M + mf mf
mf mf ][ ¨x
¨y ]+
[ C 0
0 cf ][ x˙
y˙ ]+[ K 0
0 kf][ x
y ] = [ Fe(t)
0 ]

Thanks Alot

Data
you are going to have to make the equation more clear. What are all the 0s? Try to put it up in tex.

Homework Helper
I think this is how it's supposed to look:
$$\left( \begin{array}{cc} M + m_f & m_f \\ m_f & m_f \end{array} \right) \left( \begin{array}{cc} \ddot{x} \\ \ddot{y} \end{array} \right) + \left( \begin{array}{cc} C & 0 \\ 0 & c_f \end{array} \right) \left( \begin{array}{cc} x\\ y \end{array} \right) + \left( \begin{array}{cc} K & 0 \\ 0 & k_f \end{array} \right) = \left( \begin{array}{cc} F_{e}(t)\\ 0 \end{array} \right)$$

I don't know how to use MATLAB to solve it, though.

Last edited:
J77
There should be an $$\dot{x}$$ after the damping terms (c's) and an $$x$$ after the stiffness terms (k's)...

For the simulation, first write it in first-order form.

It's quite simple to solve this forced msk system as an IVP in Matlab, check the help files on odes... amir99civil
yes. This is an equation of motion for a Tuned Liquid Column Damper with (xdot & ydot) after damping terms and (x & y) after the stiffness matrix.I don't know how i can handle the matrics if i change it to first order. If you know something then please explain a little more about the problem. How to handle the matrics to get a first order system.

The zeros 0s are 0.There is no entry where there is zero.

J77
Write:

$$u=\dot{x}$$ and $$v=\dot{y}$$

then...

$$\dot{u}=\ddot{x}$$ and $$\dot{v}=\ddot{y}$$

ie. you now have 4 first-order equations.