Converting a simple mass-spring system to state-space model, how?

1. Oct 6, 2009

cb951303

1. The problem statement, all variables and given/known data

Hi guys/girls

Professor gave this very simple homework where I need to convert the system below to a state-space model.
The system itself is represented by the equation
Code (Text):
m*x" + k*x = f(t)
Where m = 5 and k = 1. Note that, " (doublequote) is a second-order derivative.
Unfortunately I don't have the background to solve it because I slacked too much

2. Relevant equations
State-space model that we use is below:

Any help&explanation would be appreciated, thank you.

EDIT: Ok, I've just read the rules and apparently I'm not allowed to as for solutions without an attempt to solve it. Since I can't even attempt, may I ask a good place/source to start?

Last edited by a moderator: Apr 18, 2017
2. Oct 6, 2009

cb951303

attempt:

Code (Text):

5y" + 0y' + y = u

since my diff. eq. is second order, I should have 2 state variables:
Code (Text):

x1 = y
x2 = y'

so the state space model's matrixes become
Code (Text):

A = [ 0 1 ]   B = [ 0 ]
[ 1 0 ]       [ 1 ]

C = [ 1 0 ]   D = [ 0 ]

does it look ok?

3. Apr 9, 2011

MasterOfMind

Dude,

A = [0 1]
[(-k/m 0]

-k/m = -1/5 lol!