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Math Help - Particle

  1. #1
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    Particle

    <br />
x = 2 cos(3t+\frac{\pi}{6}\))<br />

    When does the particle first come to rest after t=0
    Thanks Nath
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by nath_quam
    <br />
x = 2 cos(3t+\frac{\pi}{6}\))<br />

    When does the particle first come to rest after t=0
    Thanks Nath
    At rest, velocity will be zero.
    velocity=\frac{dx}{dt}
    \frac{dx}{dt}=-6sin(3t + \frac{\pi}{6})
    Since, sin2\pi =0
    3t + \frac{\pi}{6}=2\pi
    t=\frac{11\pi}{18}

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    Malay
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  3. #3
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    Just Quickly

    Could someone please check the above as when i graphed the velocity graph i got the first point at approx 0.95 could someone show me how to prove this exact?

    Thanks Nath
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  4. #4
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    Quote Originally Posted by nath_quam
    Could someone please check the above as when i graphed the velocity graph i got the first point at approx 0.95 could someone show me how to prove this exact?

    Thanks Nath
    Malay's solution of 11pi/18 is approximately 1.92 so I'd say you made an error somewhere. Malay's method looks fine to me.

    Edit: Now that I look at it, I wonder if Malay should've set it equal to pi since that's the next time it equals 0.

    Dave
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  5. #5
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    Quote Originally Posted by malaygoel
    At rest, velocity will be zero.
    velocity=\frac{dx}{dt}
    \frac{dx}{dt}=-6sin(3t + \frac{\pi}{6})
    Since, sin2\pi =0
    3t + \frac{\pi}{6}=2\pi
    t=\frac{11\pi}{18}

    Keep Smiling
    Malay

    By using sin2\pi =0
    doesn't that find the second point
    can't we use sin\pi = 0
    and finish with t=\frac{5\pi}{18}

    Thanks Nath
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  6. #6
    Eater of Worlds
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    You're correct Nath, it first comes to rest(assuming it's moving along the positive x-axis) at t=\frac{5{\pi}}{18}

    Left of the y-axis, it first comes to rest at t=\frac{-\pi}{18}

    Add or subtract multiples of \frac{\pi}{3} to arrive at any subsequent extrema. The corresponding y values are -2 or 2.
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  7. #7
    Super Member malaygoel's Avatar
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    Quote Originally Posted by dmoran
    Malay's solution of 11pi/18 is approximately 1.92 so I'd say you made an error somewhere. Malay's method looks fine to me.

    Edit: Now that I look at it, I wonder if Malay should've set it equal to pi since that's the next time it equals 0.

    Dave
    It was a silly mistake... Sorry
    I always run into problems when dealing with trigonometric values, I am more comfortable with variables.

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  8. #8
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    Thanks for your help everyone makes mistakes
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  9. #9
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    Quote Originally Posted by malaygoel
    It was a silly mistake... Sorry
    I always run into problems when dealing with trigonometric values, I am more comfortable with variables.

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    Malay
    Not a problem. Happens to all of us!

    Dave
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  10. #10
    Super Member malaygoel's Avatar
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    Quote Originally Posted by nath_quam
    Thanks for your help everyone makes mistakes
    I am going to have my old signature:
    "An expert is one who had made all the possible mistakes in the narrowest field"
    ---Niels Bohr

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  11. #11
    Eater of Worlds
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    It's easy to overlook the little things. Anyone who has done math knows that.

    I do it all the time.
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