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[[S.H.M]] Rearranging equations Confusion, Please HELP?

  1. Jan 13, 2005 #1
    [[S.H.M]] Rearranging equations Confusion, Please HELP???

    The question that’s got me stuck
    Question: A baby of mass = 9kg bounces with a time period of 1.2s in a baby bouncer. What is the spring constant k for the bouncer? Now I know I must rearrange the formula to find k
    The formula I/the book used

    T = 2π √m ÷ k

    I do that and end up with (m × 2π) ÷ T² = k, My book on the other hand rearranges the formula as been (m × 4π²) ÷ T² = k.

    Where does the 4π² come from I do not see how 2π changes too 4π², am I missing a rule? :confused:
    Please help clarify how to get the 4π². I would ask my tutor but he is currently off sick.
    My book also does this on the previous question where I am asked to find the value of l in the equation: T = 2π √l ÷ g my book rearranges the equation to (T² × g) ÷ 4π² = k :confused:
    Again where does the 4π² come from in the original equation.

    Thanks you for your help
    Jack :confused:
     
  2. jcsd
  3. Jan 13, 2005 #2

    dextercioby

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

    Square this equation.

    Daniel.
     
  4. Jan 13, 2005 #3
    maybe a dumb question but, what exactly do you mean? if i square on both sides dont i only cancel the square root and end up with T² on the other side e.g. I'd end up with
    T² = 2π (m ÷ k) is this correct
     
  5. Jan 13, 2005 #4

    dextercioby

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    Do u agree that [tex] (ab)^{2}=a^{2}b^{2} [/tex] ?????

    If so,apply it...


    Daniel.
     
  6. Jan 13, 2005 #5
    still dont quite understand i do agree with that but am quite sure how to apply it, i feel that you wont tell me the exact answer but could you guide me a little closer???
     
  7. Jan 13, 2005 #6

    dextercioby

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    But of course i won't tell u the answer.The point is to help u find it by yourself.
    HINT:
    [tex] (2\pi)^{2} =...?? [/tex],knowing that:
    [tex] (ab)^{2}=a^{2}b^{2}[/tex]

    Daniel.
     
  8. Jan 14, 2005 #7
    Okay i think i have it: so if
    T = 2π √m ÷ k and we want to find k then:
    2π ÷ T = √m ÷ k then we square both sides
    (2π ÷ T)² = (√m ÷ k)² which simplified is 4π² ÷ T² = m ÷ k
    we then bring over the m and end up with m × 4π² ÷ T² = k
    is that correct???
     
  9. Jan 14, 2005 #8

    dextercioby

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    If it's something like that
    [tex] k=\frac{4\pi^{2}m}{T^{2}} [/tex]

    ,then it's okay.


    Daniel.
     
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