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Spring differtiation question

  1. Aug 21, 2014 #1
    1. The problem statement, all variables and given/known data
    Differentiation question on physic spring

    https://sg.answers.yahoo.com/question/index?qid=20140819111550AAvmAjH [Broken]


    2. Relevant equations


    3. The attempt at a solution

    https://www.icloud.com/photostream/#AEGY8gBYGdYO6S;2B1E78BF-9378-47B0-B87C-BD50541B4EE7

    Why I can't get the answer given: am I wrong or the answer given wrong

    Can anyoneelse work it out and see the answer
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Aug 21, 2014 #2

    BvU

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    To put it bluntly: you are wrong.

    Don't really appreciate your way of using the template, but never mind. I hope I don't get thrown out of PF for helping anyway. The hint is: integrating ##dx\over x^2+7^2## does not yield a ln. (Check by differentiating !)
     
  4. Aug 21, 2014 #3

    Simon Bridge

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    For the sake of anyone else checking in: the problem statement is:
    You are asking about C1.b.
    You have written $$1200\frac{dv}{dt} = -(v^2+49) \\ \implies t=-\int \frac{1200}{v^2+49}\;dv$$ ... you actually wrote t+c=... but the arbitrary constant gets absorbed into the integral on the RHS.

    You show no working for the integration - as BvU suggests, this is where you need to look closer.
    You appear to have got: $$\int\frac{dv}{v^2+49}=\ln(-v+7)+\ln(v+7)$$... which would be incorrect.
    It is unclear how you did that.

    As a matter of routine, you should check your solution to DEs by substituting them back.
    Do try to write out your questions in PF, it makes it easier to help you.
     
  5. Aug 21, 2014 #4

    HallsofIvy

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    [itex]-(v^2- 49)[/itex] factors as [itex](-v+ 7)(v+ 7)[/itex] but [itex]-(v^2+ 49)[/itex] does not.
     
  6. Aug 21, 2014 #5

    Simon Bridge

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    Maybe OP read ##-(v^2+49)## as ##-v^2+49## ?
     
  7. Aug 22, 2014 #6

    BvU

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    Is eggcracker still in the picture ? What of the integral of ##1\over x^2+a^2## ?
     
  8. Aug 22, 2014 #7

    Simon Bridge

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    'S only been a day ... @eggcracker: any of this helpful so far?
    More assistance with feedback.
     
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