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Need Help about Deriving Radical.

  1. Nov 19, 2011 #1
    I'm trying to derive T= 2π√m/k to become k= 4π2m/T2

    How is that happen? Can someone please explain it to me? Thanks in advance!
     
  2. jcsd
  3. Nov 19, 2011 #2

    gb7nash

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    So you're starting from:

    [tex]T = 2n \sqrt{\frac{m}{k}}[/tex]

    The first step would be to isolate the square root. How do you do that?
     
  4. Nov 19, 2011 #3
    I don't know. I tried to this T=2π (m/k)1/2 to remove the radical. I don't what's next and I'm not even sure if that is really the 1st step.
     
  5. Nov 19, 2011 #4

    HallsofIvy

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    If you have c= ab and want to "isolate" b, divide both sides by a: b= c/a.

    If have a square root, [itex]y= \sqrt{x}[/itex], square both sides: [itex]x= y^2[/itex]

    In both cases we are "undoing" what was done by doing the opposite. In "c= ab", b is not isolated because it is multiplied by a. The opposite of "multiply by a" is "divide by a". The opposite of square root is the square.
     
  6. Nov 19, 2011 #5
    Okay thanks I think I get it.

    T= 2π√m/k

    (T/2π)2 = √m/k

    T2/4π2 = m/k

    T2/4π2m = 1/k , then reciprocal both sides.
     
  7. Nov 19, 2011 #6

    HallsofIvy

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    Probably a typo- you mean [itex](T/2\pi)^2= \left(\sqrt{m/k}\right)^2[/itex]

     
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