1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Adding Sinusoids of differing Magnitute & Phases

  1. Jul 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Find A and [tex]\theta[/tex] given that:
    [tex]Acos(\omega t + \theta) = 4sin(\omega t) + 3 cos(\omega t)[/tex]
    Could someone elaborate on how to solve this. I mean it looks to me that one simply takes the magnitude of the coefficient and the inverse tangent of the same coefficients. But I feel there needs to be justification as to why we're allowed to do this.


    2. Relevant equations
    not sure.


    3. The attempt at a solution
    But the solution (according to my notes) is: [tex]A = \sqrt{4^2 + 3^2} = 5[/tex] and [tex]\theta^{-1}[/tex] = [tex]\frac{4}{3} = 53.1[/tex]

    Thanks,

    JL
     
    Last edited: Jul 7, 2009
  2. jcsd
  3. Jul 7, 2009 #2
    What if instead of

    [tex]
    Acos(\omega t + \theta) = 4sin(\omega t) + 3 cos(\omega t)
    [/tex],

    I wanted to write it as,

    [tex]
    Asin(\omega t + \theta) = 4sin(\omega t) + 3 cos(\omega t)
    [/tex],

    would the values of A and [tex]\theta[/tex] change at all?
     
  4. Jul 7, 2009 #3

    Oh, actually I think I know. The x coordinate axis is [tex]Acos(\omega t)[/tex] (negative for the negative x-axis), and the y coordinate axis is [tex]Asin(\omega t)[/tex] (negative for the negative y-axis). So this means the left side value in the equality is the actual vector, and the terms on the right are the x and y components.

    Thannks,


    JL
     
  5. Jul 7, 2009 #4

    turin

    User Avatar
    Homework Helper

    You need addition and subtraction formulas for sine and cosine (or you can use Euler's identity, but that is more advanced).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Adding Sinusoids of differing Magnitute & Phases
  1. Phase Difference (Replies: 3)

  2. Phase difference. (Replies: 2)

  3. Phase difference (Replies: 5)

Loading...