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Veriticle springs; period and mass?

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Information provided is: mass of spring, displacement, force of constant, gravity.
    so basically: m, x, k, and g
    Determine the relationship between the period and mass

    so how do i find T?

    2. Relevant equations

    T= seconds/cycles
    T= 2π(sqrt(m/k))


    3. The attempt at a solution

    I used T= seconds/cycles and got 0.47
    BUT. when i used 2π(sqrt(m/k)) I got 0.39

    shouldnt both formulas be right?
    why are my answers different?
    Thanks!
     
  2. jcsd
  3. Apr 14, 2012 #2

    tiny-tim

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    sho

    hi wow22! :wink:
    show us your full calculations, and then we'll see what went wrong :smile:
     
  4. Apr 14, 2012 #3
    m=100g = 0.1kg
    g= 9.8 m/s^2
    k= 26.6

    so when
    2π(sqrt(m/k))
    =2π(sqrt(0.1/26.6))
    0.39

    seconds/cycles
    t=4.7s
    cycles=10

    so
    t/cycles= 4.7s/10
    =0.47
    .. :s
     
  5. Apr 14, 2012 #4

    tiny-tim

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    where do 10 and 4.07 come from? :confused:

    and what is this spring doing?
     
  6. Apr 14, 2012 #5
    We calculated the time it takes for the hanging mass attached to the spring To fall and make 10 cycles . So tits 10 cycles in 4.7s
     
  7. Apr 14, 2012 #6

    tiny-tim

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    you mean you measured it?

    then some of your other data must be wrong :confused:
     
  8. Apr 14, 2012 #7
    Yeah.... But we double checked with other groups and it was relatively the same .. But ideally, If I had the correct information, should both of finding period work ? :S
     
  9. Apr 14, 2012 #8

    tiny-tim

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    yes of course!

    probably the k they gave you was wrong :smile:
     
  10. Apr 14, 2012 #9
    Oh actually we had to find k too :S

    But thanks again tiny-tim :D
     
  11. Apr 14, 2012 #10
    Can someone just check if these are correct:

    the amplitude does not affect the period of vibration within a spring because the period will only change if the mass or force constant changes.

    a mass experiences dynamic equilibrium when the mass is hanging on the spring at its most stretched/compressed displacement (so when v=0m/s)

    a mass experiences its maximum speed when it is in the middle of its stretched displacement

    the acceleration of the mass is constant because the only acceleration acting on the mass is gravity

    (this does the same thing with the verticle spring stuff up there^)
     
  12. Apr 15, 2012 #11

    tiny-tim

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    yes :smile:
    i know what you mean (and it's correct), but that's not called dynamic equilibrium

    dynamic equilibrium has to be equilibrium, ie balanced forces (see http://en.wikipedia.org/wiki/Dynamic_equilibrium), and this isn't
    sorry, this is nonsense :redface:

    acceleration does not act, it just is

    one body has only one acceleration

    there are two forces on the body … one is constant (gravity), the other isn't

    the acceleration is certainly not constant, it's harmonic, and proportional to the displacement
     
  13. Apr 15, 2012 #12
    @tiny-tim : how? the maximum velocity is at the mean position. So even if it is at the midpoint of stretched displacement, it does not have max velocity. So I think second one is wrong, isn't it?
     
  14. Apr 15, 2012 #13

    tiny-tim

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    they're the same, aren't they? :confused:

    it's simple harmonic motion, so the maximum speed is at the midpoint
     
  15. Apr 15, 2012 #14
     
  16. Apr 15, 2012 #15
    :$ Sorry i'm kind of lost..
    So when IS it in dynamic equilibrium? it's supposed to be when the two forces acting on it are equal no? so gravity=force of tension i was geussing..

    Thanks!
     
  17. Apr 15, 2012 #16

    tiny-tim

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    i wouldn't apply it to this case, since the system is continually changing, but if you did, it would be when the forces are balanced, and the system isn't changing

    for example, there's dynamic equilibrium for the water-air mixture in a sealed container: water molecules are continually leaving the liquid water (evaporating) and joining the air, while other water molecules are leaving the air and joining the liquid water …

    overall, the proportion of water in the air stays the same, so there's equilibrium, but since the actual molecules are dodging to and fro, the equilibrium is dynamic​
     
  18. Apr 15, 2012 #17
    Okay thanks! Well our lab asks us when it is in dynamic equilibrium :S do I should write that there is home?
     
  19. Apr 15, 2012 #18

    tiny-tim

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    i've no idea :confused:

    what has your professor given you as the definition of dynamic equilibrium?
     
  20. Apr 15, 2012 #19
    when forces are balanced, the mass will move at a constant velocity.
     
  21. Apr 15, 2012 #20

    tiny-tim

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    but there's no constant velocity here :confused:

    (unless either

    i] we regard the velocity at any point as instantaneously constant, or

    ii] it means that the magnitude of the velocity is instantaneously at a maximum or minimum)​
     
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