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    Yo,

    I basically have this question: 5. (a) Use the final value theorem to determine the value of y(∞), without actually solving the ODEy'+y=1, y(0) = 0
    The Laplace transform of the ODE is: sG(s)+G(s)=1/s G(s)=1/s(s+1)

    I know the answer is 1, I've solved the ODE and got the answer as 1 (when t approaches infinity) however G(0)=infinity, which can't be right, what have I done wrong?
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    (Original post by zooloowarrier)
    Yo,

    I basically have this question: 5. (a) Use the final value theorem to determine the value of y(∞), without actually solving the ODEy'+y=1, y(0) = 0
    The Laplace transform of the ODE is: sG(s)+G(s)=1/s G(s)=1/s(s+1)

    I know the answer is 1, I've solved the ODE and got the answer as 1 (when t approaches infinity) however G(0)=infinity, which can't be right, what have I done wrong?
    I have not looked at this with pen and paper

    the initial/final value theorem says

    Limit (sf(s)) as s tends to zero equals F(t) as t tends to infinity

    or

    Limit (sf(s)) as s tends to infinity equals F(t) as t tends to zero


    I will look at it later but
    take the transform
    then take limits as sf(s) tends to 0
    might require some manipulation
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    (Original post by TeeEm)
    I have not looked at this with pen and paper

    the initial/final value theorem says

    Limit (sf(s)) as s tends to zero equals F(t) as t tends to infinity

    or

    Limit (sf(s)) as s tends to infinity equals F(t) as t tends to zero


    I will look at it later but
    take the transform
    then take limits as sf(s) tends to 0
    might require some manipulation
    Thanks, I'll give it another go
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    (Original post by zooloowarrier)
    Thanks, I'll give it another go
    Just finished dinner
    it is actually a few lines
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    (Original post by TeeEm)
    Just finished dinner
    it is actually a few lines
    I've gone over it twice now and still getting the same thing :/
    1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
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    (Original post by zooloowarrier)
    I've gone over it twice now and still getting the same thing :/
    1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
    give me 5 minutes to write it
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    (Original post by TeeEm)
    give me 5 minutes to write it
    Thanks for your help
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    (Original post by zooloowarrier)
    I've gone over it twice now and still getting the same thing :/
    1/s(s+1) definitely tends to infinity so I must have gone wrong with the actual transform but I can't see where
    you should really post maths in the maths room
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    (Original post by TeeEm)
    you should really post maths in the maths room
    I'll keep that in mind for the next time
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    (Original post by zooloowarrier)
    I'll keep that in mind for the next time
    here it is
    Attached Images
     
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    (Original post by TeeEm)
    here it is
    My bad, I didn't read/apply the theorem properly.

    Thank you for your help!
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    (Original post by zooloowarrier)
    My bad, I didn't read/apply the theorem properly.

    Thank you for your help!
    never mind


    all the best
 
 
 
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