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Math Help - Wave Motion and Velocity

  1. #1
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    Wave Motion and Velocity

    A buoy oscillates in simple harmonic motion y = A cos \omega t as waves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds.
    a) Write an equation describing the motion of the buoy if it is at its high point at t = 0.
    b) Determine the velocity of the buoy as a function of t.

    First of all, what does A even stand for? Also, generally stumped about this.
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  2. #2
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    Quote Originally Posted by seuzy13 View Post
    A buoy oscillates in simple harmonic motion y = A cos \omega t as waves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds.
    a) Write an equation describing the motion of the buoy if it is at its high point at t = 0.
    b) Determine the velocity of the buoy as a function of t.

    First of all, what does A even stand for? Also, generally stumped about this.
    A is the amplitude of motion ... the maximum distance from equilibrium.

    in this case A = \frac{3.5}{2} = \frac{7}{4}

    \omega = \frac{2\pi}{T} = \frac{2\pi}{10} = \frac{\pi}{5}

    y = \frac{7}{4}\cos\left(\frac{\pi}{5} \cdot t\right)<br />

    the velocity function is the derivative of the position function ...

    v = -\frac{7\pi}{20}\sin\left(\frac{\pi}{5} \cdot t\right)<br />
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    All makes since except  A = \frac {3.5}{2} . Why divide by two?

    Thanks. You've helped a lot.
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    Quote Originally Posted by seuzy13 View Post
    All makes since except  A = \frac {3.5}{2} . Why divide by two?

    Thanks. You've helped a lot.
    because equilibrium is half-way between the high and low positions
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    Okay. I understand now. Thank you so much!
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