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ranyai12

  • 2 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' =

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  1. TuringTest
    • 2 years ago
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    I am thinking that there is a typo... are you sure it says rewrite as \[y=x\]?

  2. mahmit2012
    • 2 years ago
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    y=x'

  3. mahmit2012
    • 2 years ago
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    and we should find out (x,y)=(x,x')=state space vector.

  4. ranyai12
    • 2 years ago
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    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
    • 2 years ago
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    |dw:1344182958485:dw|

  6. ranyai12
    • 2 years ago
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    whats whats y= to?

  7. mahmit2012
    • 2 years ago
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    |dw:1344183055225:dw|

  8. ranyai12
    • 2 years ago
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    wait howd you solve that?

  9. ranyai12
    • 2 years ago
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    yea i got the critical points but I used the jacobie eigenvalue

  10. ranyai12
    • 2 years ago
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    i mean jacoby value

  11. mahmit2012
    • 2 years ago
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    the problem has three critical points that I showed you.

  12. ranyai12
    • 2 years ago
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    how did ou see that x'=y

  13. mahmit2012
    • 2 years ago
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    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
    • 2 years ago
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    whats space vector?

  15. mahmit2012
    • 2 years ago
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    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
    • 2 years ago
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    So (x,v,a)=(x,x',x") is a state space vector.

  17. ranyai12
    • 2 years ago
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    oh ok! thank you!!

  18. mahmit2012
    • 2 years ago
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    you're welcome.

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