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Homework Help: Freq response of forced sinusoidal motion:

  1. Nov 28, 2009 #1
    The book I am currently reading derives the response of an electron to an applied sinusoidal field as:

    1/[1 + 2i (w - wa)/g] = 1 / (1 + i delta)

    where w and wa are the induced and resonance response frequencies and g the damping constant.

    And delta = 2 (w - wa)/g

    Up to this point there is no problem. But the book then states that the amplitude squared or power response has the form:

    1/[1 + {2 (w - wa)/g}2 ] = 1 / (1 + delta2)

    And here is the problem.... if you square the first equations listed you don't get what they give as the power response. I think the answer should be:

    1 / (1 + 2 i delta - delta2)

    Is there some assumption I am missing, its not just the imaginary term is missing the sign is wrong for the squared term??

    Thanks for any help!
  2. jcsd
  3. Nov 28, 2009 #2


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    Staff Emeritus
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    For complex amplitudes, one squares the absolute value of the amplitude to get the power response.
  4. Nov 30, 2009 #3
    :redface: Thanks!
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