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Determining a sinusodial equation

  1. Nov 30, 2009 #1
    1. The problem statement, all variables and given/known data

    A boat is tied up at a dock and bobs up and down. The vertical distance between its high and low point is 1.8 m and the cycle is repeated every 4s.

    a) Determine a sine equation to model the vertical position, in metres, of the boat versus the time, in seconds.

    b) Use your model to determine when, during each cycle, the boat is 0.5 above its mean position. Round your answers to the nearest hundreth of a second.

    2. Relevant equations

    y= a sin (k(x-d))+c

    Period Length = 2 pi/k

    a = amplitude

    k = horizonatl stretch/compression

    d= horizontal translation

    c= vertical translation

    3. The attempt at a solution

    Not sure If I am correct so far, but I found the amplitude and k value.

    A=0.9 (Divided 1.8 by 2) and K = pi/2 ( I found that doing PL = 2pi/k)

    Not sure how to get d or c though.

    Would appreciate any help. Thanks
     
  2. jcsd
  3. Nov 30, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Excellent! As for "d" and "c", they depend on your choice of coordinate system: if you take y= 0 to be the mean position of the boat, the c= 0. If, also, you choose t= 0 to be when the boat is at that mean position, then d= 0.
     
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