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What frequency of vibration is required?

  1. Mar 5, 2007 #1
    1. The problem statement, all variables and given/known data

    (a) acceleration amplitude of 100 ms−2 with a vibration amplitude of 5.0 cm.

    (i) What frequency of vibration is required?
    (ii) What is the maximum speed ?
    (iii)What is the time delay between the points of maximum acceleration and
    of maximum speed?

    2. Relevant equations

    speed= f * wavelength

    f= 1/ time period

    3. The attempt at a solution

    (i)

    a= -2*pi*f*x

    100= -2*pi*f*0.05

    400=-pi *f

    400/ -3.141= f

    f= - 127.32 Hz

    (can frequency be minus)??

    (ii)

    speed = integral of accelration
    a= -2*pi*f*x

    speed= f * wavelength

    (iii)

    time delay
    f= 1/ time period
    t= 1/ - 127.32 Hz
    t= 0.00785423
     
    Last edited: Mar 5, 2007
  2. jcsd
  3. Mar 5, 2007 #2
    Seems to me like this is a problem in simple harmonic motion. The acceleration to be found is the acceleration of a point on the medium that the wave is travelling through. As a wave travels through a medium it causes the particles within that medium to oscillate, each one about their own equilibrium position.
    Smple harmonic motion is the simplest form of oscillation. Its defining equation is:-

    a= -2*pi*f*x

    where
    a = acceleration
    f= frequency
    x= displacement from equilibrium position (max value = amplitude)

    Hope this gets you started.
     
  4. Mar 5, 2007 #3
    a= -2*pi*f*x

    100= -2*pi*f*0.05

    400=-pi *f

    400/ -3.141= f

    f= - 127.32 Hz

    (can frequency be minus)??
     
  5. Mar 5, 2007 #4
    (ii)

    speed = integral of accelration
    a= -2*pi*f*x

    speed= f * wavelength

    f= - 127.32 Hz
     
  6. Mar 5, 2007 #5
    (iii)

    time delay
    f= 1/ time period
    t= 1/ - 127.32 Hz
    t= 0.00785423

    is this correct (i, ii, iii)
     
  7. Mar 6, 2007 #6
    well is this correct???
     
  8. Mar 6, 2007 #7

    hage567

    User Avatar
    Homework Helper

    "a= -2*pi*f*x"

    This is not an equation for acceleration. Check the units, they don't work out. Maybe you didn't copy it from your book correctly? Go look it up again.

    Please try to be patient about waiting for replies. :smile:
     
    Last edited: Mar 6, 2007
  9. Mar 6, 2007 #8
    (a) acceleration amplitude of 100 ms−2 with a vibration amplitude of 5.0 cm.
    (i) What frequency of vibration is required?

    u gave me this equation at top of this page=

    a= -2*pi*f*x

    i have used it....doesnt work..??
     
  10. Mar 6, 2007 #9
    a= -2*pi*f*x

    where
    a = acceleration
    f= frequency
    x= displacement from equilibrium position (max value = amplitude)

    Hope this gets you started.
    --------------------------------------------------------

    a= -2*pi*f*x
    100=-2*3.141*0.05* f
    f= 317 Hz...

    is this correct...using the formula u gave
     
  11. Mar 6, 2007 #10

    hage567

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    Homework Helper

    I'm not the one that gave you the formula. You started off with it yourself by the looks of things. But it doesn't matter, it is still wrong.
    Look at it carefully. The units work out to those of velocity, not acceleration. Check it. So, what would the right equation be? It's very similar.
     
  12. Mar 6, 2007 #11
    sorry HAGE,

    apeeling gave me the INCORRECT acceleration formula,

    well if the formula is velocity then u differtiate to get accelration.

    But i dont want to start off with INCORECT formula.

    Can you please give me the correct formula to start with.
    -------------------------------------------------------------

    w= 2*pi*f

    accelration= -W^2 x

    100= -w^2 * 0.05
    2000= -W^2
    +- square root of 2000= w

    w=2*pi*f

    +- square root of 2000= 2*pi*f

    +- square root of 2000/2*pi= f

    ---------------------------------------
     
  13. Mar 6, 2007 #12

    hage567

    User Avatar
    Homework Helper

    "accelration= -W^2 x"

    Get rid of the negative sign, I don't understand why it's there. Do that, and you have the right equation.
     
  14. Mar 6, 2007 #13
    formula booklet states a minus sign.

    Does that depend where u take the point of refrence?

    so doing this kind of problem you leave minus sign. What is the signifcan of minus sign again.

    -----------------------------------------------------------------

    (ii) What is the maximum speed ?
    a= v w
    100= v w

    would that be correct method

    ---------------------------------------
    (iii)What is the time delay between the points of maximum acceleration and
    of maximum speed?

    what formula needed to work at time delay
     
  15. Mar 6, 2007 #14

    hage567

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    Homework Helper

    For the maximum acceleration I would think it would be positive. But whatever, go by what you think.
    (b): Yeah, i guess that works. You could also use the equation for speed that you were using by accident for acceleration.
    (iii): Have you tried to come up with it yourself?
     
  16. Mar 6, 2007 #15
    (iii)
    x= Asin (wt)

    v= Awcos (wt)
    100/w= v

    100= Aw^2 (wt)

    A is a constant, what will this constant be?

    would this be right equation for (iii)
     
  17. Mar 6, 2007 #16

    hage567

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    Homework Helper

    I don't understand what you're trying to show. What will what constant be? You can reason this out as well, without any math. So if you can get both to agree then you probably have it right.

    Do watch out for the signs in this, you just have to be careful what case you are taking (like at max acceleration, or just at some point x that is not at max acceleration). Sorry I know that isn't very clear, but I think you're aware of it anyway.
     
    Last edited: Mar 6, 2007
  18. Mar 7, 2007 #17
    well is was that the corect formual to work out time delay.

    i quoted the formula...from formula booklet
     
  19. Mar 14, 2007 #18
    need help on this question??
     
  20. Mar 15, 2007 #19
    i)
    w= 2 pi f

    accerleation= A w^2
    100 = 0.05 * w^2
    w= 44.721

    44.721= 2 pi f
    f= 7.11 Hz

    ii)
    V= Aw
    = 0.05* 44.721
    =2.23 m/s

    is this corect?
     
  21. Mar 16, 2007 #20
    urgent help required is this CORRECT???
     
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