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Homework Help: Simple Harmonic motion of sand grain

  1. Sep 14, 2008 #1
    Sand grains rest on a horzontal plate. The plate vibrates in the vertical plane with SHM of amplitude 1.5mm at a fixed frequency with acceleration equal to free fall (9.8ms^-2).

    What will happen to the grains of sand when the frequency of vibration is increased?

    I am unsure of how to tackle this problem. Will the amplitude of oscillation decrease? My working is below:

    max acceleration = amplitude*((2*pi*f)^2)


    If f increases, with max acceleration the same, the amplitude decreases. Is this reasoning and answer correct?

    Thanks
     
    Last edited: Sep 14, 2008
  2. jcsd
  3. Sep 14, 2008 #2

    Doc Al

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    I suspect they mean "while keeping the amplitude the same". What happens then? (Hint: What's special about the initial max acceleration?)
     
  4. Sep 14, 2008 #3
    Im not sure... the acceleration of free fall is surely the maximum acceleration that the sand can have isn't it?

    Thanks
     
  5. Sep 14, 2008 #4

    Doc Al

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    On the way down it is. And that's the key. What happens if the acceleration of the plate exceeds the acceleration due to gravity?
     
  6. Sep 14, 2008 #5
    It will seize to oscillate with SHM?
     
  7. Sep 14, 2008 #6

    Doc Al

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    Actually, yes. But they're looking for something much more basic (I presume). If you were watching the sand/plate vibrate, you'd immediately notice when the acceleration exceeded g. Why?
     
  8. Sep 14, 2008 #7
    The plate and sand particles would seperate?
     
  9. Sep 14, 2008 #8

    Doc Al

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    Exactly! You'd see the sand particles start to bounce around.
     
  10. Sep 14, 2008 #9
    That makes sense! Thank you so much!
     
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