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How do I integrate this?

  1. Sep 21, 2005 #1
    An L-C circuit will undergo resonance, with the current varying sinusoidally, where:
    I(t) = I*cos(omega*t)

    I keep getting stuck with an answer of I*t*sin(omega*t)

    Can't find anything on the standard table of integrals that would indicate this is incorrect

    :confused:
     
  2. jcsd
  3. Sep 21, 2005 #2

    Fermat

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    How did you get the answer of I*t*sin(omega*t)
     
  4. Sep 21, 2005 #3
    I*cos(omega*t)

    omega's just a constant then? I'll call it a

    I*cos(at)

    I's a constant too, so you'll only integrat cos(at)

    which should be sin(at)/a

    so I*sin(omega*t)/omega?

    Other possibility, since I'm not sure myself, is that you can express omega as a function of time, can't you? (2pi*frequency)and frequency is like 1/t or something. I dunno, I think the first way's right

    Edit: Wait, I isn't a constant, well whatever, I'll leave this post up here for learning purposes but methinks it's rubbish
     
  5. Sep 21, 2005 #4

    Fermat

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    That looks correct. I wasn't sure what you were integrating.

    omega isn't a funtion of time - it is a constant.

    omega is only a funtion of time if it varies with time.
    frequency isn't a function of time either, but usually, a constant value. frequency is simply the rate at which something changes wrt time. But that rate of change is constant!!
     
  6. Sep 22, 2005 #5
    That I is a constant - it's the value of the current at time t = 0 (usually).
     
  7. Sep 22, 2005 #6
    Thanks I'll give that a shot. Sorry for the confusion, omega was a constant (angular frequency). I'm worried about how much high school stuff I've already forgotten :eek:

    I wasn't sure how to properly intergrate in that case.

    I tried looking it up, but could only find the simple cases (i.e. integrate sin x = cos x)
     
    Last edited: Sep 22, 2005
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