A 2nd Order ODE

  • #1
Dear All,

I have a Problem about a 2nd order ode. I dont 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
 

Answers and Replies

  • #2
998
0
you are going to have to make the equation more clear. What are all the 0s? Try to put it up in tex.
 
  • #3
Mute
Homework Helper
1,388
10
I think this is how it's supposed to look:
[tex]\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)[/tex]

I don't know how to use MATLAB to solve it, though.
 
Last edited:
  • #4
J77
1,083
1
There should be an [tex]\dot{x}[/tex] after the damping terms (c's) and an [tex]x[/tex] 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...

:smile:
 
  • #5
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 dont 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.
 
  • #6
J77
1,083
1
Write:

[tex]u=\dot{x}[/tex] and [tex]v=\dot{y}[/tex]

then...

[tex]\dot{u}=\ddot{x}[/tex] and [tex]\dot{v}=\ddot{y}[/tex]

ie. you now have 4 first-order equations.
 

Related Threads on A 2nd Order ODE

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
7K
  • Last Post
Replies
3
Views
4K
Replies
4
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
951
Top