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Oscillation Problem -- Why does my way not work?

  1. Apr 1, 2017 #1
    1. Problem Description:
    A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest at a position y. The object is then released from y and oscillates up and down, with its lowest position being 10cm below y.
    What is the frequency of the oscillation?

    2. Relevant equations
    F=kx; w= sqroot k/m ; f= w/2pi ;

    3. I know that the right answer to the problem is 2.2 Hertz and I know how you could solve it using energy however I was wondering why the following does not give me the right answer. Is my math just wrong or is it a conceptual problem?

    My Way:

    mg = kx ; x= .1m
    mg = k (.1)
    (9.8 /.1) = k/m
    k/m = 98

    w = sq-root k/m
    w = sq-root (98)
    w = 9.89

    f = w/(2pi)
    f= (9.89)/(2pi)
    f= 1.57 Hz

    This is obviously not the right answer. I hope you can give me an explanation as to why it's not.
    Thanks in advance!
  2. jcsd
  3. Apr 1, 2017 #2
    Why did you equate weight and spring force?
  4. Apr 1, 2017 #3
    I don't no if this assumption is true, but I just thought that the mass/spring system's equilibrium point was at .1m and at that point the force of the spring and the force due to gravity should be equal (but in opposite direction).
  5. Apr 1, 2017 #4
    Do you know the dynamics of oscillation? Think of a pendulum. What happens at its extreme point?
  6. Apr 1, 2017 #5
    Ok, I think I see where the problem is. The distance x can't be the equilibrium point because when smth oscillates, it goes beyond its equilibrium point. So F of the spring can't be equal to mg, right?
  7. Apr 1, 2017 #6
    That is correct.
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