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    clairegibraltar's Avatar
    clairegibraltar Posts: 1, Reputation: 1
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    #1

    May 17, 2007, 07:23 AM
    Equations related to simple harmonic motion
    This is a really urgent question!

    If x=Acos2 pie ft,
    then how does f affect x?
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #2

    May 17, 2007, 08:49 AM
    sinusoidally, according to the equation.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #3

    May 17, 2007, 10:25 AM
    Increase the frequency f, and x cycles faster.
    SameOldSituation's Avatar
    SameOldSituation Posts: 66, Reputation: 32
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    #4

    May 22, 2007, 12:16 PM
    I'm a little confused. I thought x was displacement. If any side of the right part of the equation is increased, obviously so is the left. Then, wouldn't displacement be increased? Ie---the total "distance" covered? (Yes, I know it osciallates back and forth, and thus in a given time, increasing frequency will increase how fast it cycles.)

    "x cycles faster" incorporates time... do you say that because the equation is x as a fuction of t? Would it be wrong to simply say, "as frequency increases, so does displacement," and just leave it at that?
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #5

    May 22, 2007, 12:22 PM
    No, because the f and t are inside the cos. X can be 0 at a given f, depending on t.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #6

    May 22, 2007, 12:34 PM
    It would be easier to see if the original equation had been written out properly:



    Here t is time (typically seconds), f is frequency (cycles/second), A is the amplitude (meters), and x(t) is the displacement as a function of time. You can see that this function cyces from -A to +A in a sinusoid pattern at a frequency of f cycles per second. Increasing f does nothing to the maximum value that x(t) can reach.
    tactoth's Avatar
    tactoth Posts: 1, Reputation: 1
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    #7

    May 22, 2007, 11:57 PM
    Comment on ebaines's post
    The formula looks clear
    SameOldSituation's Avatar
    SameOldSituation Posts: 66, Reputation: 32
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    #8

    May 23, 2007, 06:41 AM
    Yeah... that makes sense. I think I was confusing amplitude and disp. Thanks.
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