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Frequnecy of Combined Motion

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the frequency of the combined motion of sin(3t) - cos(Pi t)


    2. Relevant equations
    Cos(A) - Cos(B) = -2sin([A+B]/2)sin([A-B]/2)
    f=1/T
    Omega=2Pi/T

    3. The attempt at a solution
    sin(3t) - cos(Pi t) =
    cos(3t - (Pi/2)) - cos(Pi t) =
    -2sin({t[3 + pi]/2} - (pi/4))sin({t[3 - pi]/2} - (pi/4))

    Now, I tried taking the average of omega(1) and omega(2), but this is not correct.
    I am confused on what the next step is.
     
  2. jcsd
  3. Sep 7, 2010 #2

    gabbagabbahey

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    When you have two sinusoidals multipled together, and the frequency of one is much larger/faster than the frequency of the other, the overall signal appears to oscillate at the smaller/slower frequency, and is modulated by the much faster sinusoid (you end up with a "bumpy" sinusoid where the bumps have a very fast frequency, but their amplitude is much smaller and they are often almost unnoticable). Try graphing your signal over a very short (much less than the period of the slower sinusoid) and a longer (at least ione full period of the slower sinusoid) time interval to better visualize what's going on.
     
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