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Finding Period from a and v

  1. Mar 7, 2013 #1
    This question has me completely baffled. So here it goes:


    A spring oscillates with a period T and an Amplitude A. Solve for period and amplitude in terms of a[max] and v[max]

    My math always comes out with an answer I know is wrong. Can anyone be kind enough to assist me?


    Much appreciated.
     
  2. jcsd
  3. Mar 7, 2013 #2

    SammyS

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    Hello Shinaolord. Welcome to PF !

    You really haven't given us enough detail to help.

    Also, show us how you are getting your results.
     
  4. Mar 7, 2013 #3
    That's literally all it gives you. It says to "solve for the amplitude and period in terms of a[max] and v[max]. It's purely conceptual, which I think is the hindrance. Does that Help?


    EDIT: Thank you for the welcome! Much appreciate, SammyS.

    My results, via Algebra and substitution, is as follows:

    a[max]=Aw^2, so A=a[max]/w^2
    and V=-Aw, so V also =-(a[max]/w^2)w
    which simplifies to v[max]=-(a[max]/w)
    now, w=2[pi]/T, so v[max]=-(a[max]T/(w[pi])
    so T=-v[max]w[pi]/a[max]
    This doesn't seem right...Is my math or reasoning wrong? Am i just not seeing it?
     
    Last edited: Mar 7, 2013
  5. Mar 7, 2013 #4

    SammyS

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    If amax = Aω2, then it should be true that vmax = Aω .

    ( amax and vmax should both be positive. )

    Doesn't it follow that ω = amax/vmax ?
     
  6. Mar 8, 2013 #5
    Yes, correct, but for period the back of my book says t=v[max]^2/a[max].
    This is all new to me, apologies if I seem "stupid"
     
  7. Mar 8, 2013 #6
    Never mind I see

    Sorry for do, my iPad wont let me edit
     
  8. Mar 8, 2013 #7

    SammyS

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    That looks more like amplitude than period.

    [itex]\displaystyle \frac{v_\text{max}^2}{a_\text{max}}=\frac{A^2 \omega^2}{A\omega^2}=A\ .[/itex]

    Whereas we had   ω = 2π/T .

    So, if [itex]\displaystyle \ \omega=\frac{a_\text{max}}{v_\text{max}}\,,\ [/itex] then [itex]\displaystyle \ T=2\pi\frac{v_\text{max}}{a_\text{max}}\ .[/itex]
     
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