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Is the derivative in my textbook correct here?

  1. Sep 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Principle of Cons Ener.JPG

    2. Relevant equations
    d/dx

    3. The attempt at a solution
    d/dx (T) = d/dx(1/2mx'2) = mx''
    d/dx(U) = d/dx(1/2kx2) = kx' ≠ kx

    It's probably me who made an error because I know that that equation (2.3) is the one I should be getting, but I don't understand how they did it because potential energy relies on position, so the derivative has to be a velocity vector.
     
  2. jcsd
  3. Sep 12, 2016 #2

    gneill

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    Staff: Mentor

    Here x is a function of t and the derivatives should be with respect to t. That's what x' implies.
     
  4. Sep 12, 2016 #3

    NascentOxygen

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    Staff: Mentor

    (2.6) shows differentiation with respect to time. Your working is erroneously using differentiation with respect to x.
     
  5. Sep 12, 2016 #4
    Oh right, it's x(t)... I guess the caffeine hasn't kicked in because that was really basic. Thank you!
     
  6. Sep 12, 2016 #5

    gneill

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    Staff: Mentor

    No worries. Enjoy your coffee!
     
  7. Sep 12, 2016 #6

    NascentOxygen

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    Staff: Mentor

    I think (2.3) starts out as ##m \ddot x \dot x + k x \dot x = 0## and the common factor ##\dot x## can be cancelled from both sides.
     
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