## ranyai12 3 years ago Consider the spring model x''−3x+3(x^3)=0 where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in x and y=x. x' = y' =

1. TuringTest

I am thinking that there is a typo... are you sure it says rewrite as \[y=x\]?

2. mahmit2012

y=x'

3. mahmit2012

and we should find out (x,y)=(x,x')=state space vector.

4. ranyai12

idk thatswhat tge directions say exactly i just copied and pasted we also had to solve for critical points which i already did

5. mahmit2012

|dw:1344182958485:dw|

6. ranyai12

whats whats y= to?

7. mahmit2012

|dw:1344183055225:dw|

8. ranyai12

wait howd you solve that?

9. ranyai12

yea i got the critical points but I used the jacobie eigenvalue

10. ranyai12

i mean jacoby value

11. mahmit2012

the problem has three critical points that I showed you.

12. ranyai12

how did ou see that x'=y

13. mahmit2012

Those of the problems like yours we should define a state space vector that includes independent component ,usually x and its derivatives are selected as components.

14. ranyai12

whats space vector?

15. mahmit2012

state space vector is a vector which include all independent variable in a system. for example place velocity . acceleration are three component require to know in a third order system.

16. mahmit2012

So (x,v,a)=(x,x',x") is a state space vector.

17. ranyai12

oh ok! thank you!!

18. mahmit2012

you're welcome.