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Determine the equation when given a graph

  1. Dec 11, 2012 #1
    1. The problem statement, all variables and given/known data
    graph.jpg
    The graph goes on for ever in both directions and we know that it's in the form
    y=Asin(Bx+C)

    2. Relevant equations



    3. The attempt at a solution

    I'm not sure what to do here. The amplitude is easy, it's 2.

    C/B = Period
    Correct?

    I'm at a loss here.
     
  2. jcsd
  3. Dec 11, 2012 #2

    Mark44

    Staff: Mentor

    Or y = A sin(B(x + C/B))
    No. If you had y = sin(x + D), the period would be ##2\pi##.
    If you had y = sin(2(x + D)), the period would be ##2\pi/2##, right?


     
  4. Dec 11, 2012 #3
    Hmm I'm not sure I'm following your logic here. What throws me off is the fact that I have no pies on the X-axis. I have no idea how to start calculating the period.

    If I had a 2pi it would be easy enough, I'd just see how many cycles the graph completes in a 2pi interval.
     
  5. Dec 11, 2012 #4

    Mark44

    Staff: Mentor

    From your graph, can you estimate what the period is?
     
  6. Dec 11, 2012 #5
    P=12/13

    ?
     
  7. Dec 11, 2012 #6

    Mark44

    Staff: Mentor

    ???

    How did you get that?
     
  8. Dec 11, 2012 #7

    Mark44

    Staff: Mentor

    Your graph shows slightly more than one period of this function.
     
  9. Dec 11, 2012 #8
    I graphed it by hand since I remembered it of my final today and I couldn't solve it. Assume that the graph goes on forever.

    Hmm okay let me retry.
    Every integer is divided into 6 parts as you can see from the graph.
    When calculating the period I start from the 1/6 and go to 13/6 where the graph repeats itself.
    This means that the period is 12/6 = 2?
    The phase shift is 1/6 so the end result would be

    y=2sin(2x-1/6)

    Correct?

    I feel like I'm missing a pi somewhere.... Is it y=2sin(pi(x)-1/6) ?
     
    Last edited: Dec 11, 2012
  10. Dec 11, 2012 #9

    Mark44

    Staff: Mentor

    Yes.
    No, but you're getting closer than you were before.

    Let's look at a simpler example, y = sin(2x). Its period is ##2\pi/2 = \pi##. Your function has a period of 2, so the number that multiplies x needs to be what?
    This is very close. If you want to shift the graph of y = sin(2x) to the right by 1/2, it would be y = sin(2(x - 1/2)). Does that give you an idea?
     
  11. Dec 11, 2012 #10
    Hmm... Okay. My period is

    2pi / 2 = pi.
    y=2sin(pi(x))

    Now, to phase shift 1/6 of a unit I do

    y = 2sin(pi(x) - pi/6)

    ?
     
  12. Dec 11, 2012 #11

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That looks right.
     
  13. Dec 11, 2012 #12
    Thanks a bunch. Much appreciated. I totally bombed my final but at least I walked away with some new knowledge.
     
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