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Wave Problem - Phase Shift

  1. Sep 6, 2013 #1
    1. The problem statement, all variables and given/known data
    1. A signal of the form x(t) = A cos(ω0t + φ) is plotted below. From the plot, deduce the following:
    (a) the amplitude A, (b) the period T0, (c) the radian frequency ω0, and (d) the phase φ in radians. For part (e), find f0 in Hz by converting the radian frequency from part (c). For part (f), convert the phase from part (d) to degrees.



    2. Relevant equations



    3. The attempt at a solution

    a) Amplitude = 6 (inspection)
    b) Period = (218.75ms + (-31.25ms)) = 250ms
    c) ω=2π/T = 2π / 0.250s = 8π rad/sec
    d) dφ=2π/dt = -8π/125
    e) frequency = ω/2π = 8π/2π = 4Hz
    f) deg = 180 φ/2π = 5.76 deg

    y(t) = 6cos(8πt - 8π/125)

    So i am not sure on my calculation for the phase shift.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Sep 6, 2013 #2

    ehild

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    It is a typo in b) (period) but the result is correct. The "+" should be "-".

    As for the phase constant: The signal has the form Acos(ωt+φ) It is maximum when ωt+φ=0, or integer times 2pi. Nearest to t=0, there is a maximum at t=-31.25 ms. Take ωt+φ=0, and substitute -31.25 for t.

    ehild
     
    Last edited: Sep 7, 2013
  4. Sep 6, 2013 #3

    rude man

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