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Finding the amplitude

  1. Dec 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    I have the following harmonic function:

    [tex]
    V(t)=A\cos(\omega t)\exp(-Ct),
    [/tex]


    where C is a constant, and A is the amplitude. I need to find the time t, where the amplitude is A/2. This gives me:

    [tex]
    V(t)=A\cos(\omega t)\exp(-Ct) = \frac{A}{2},
    [/tex]

    but how do I solve this equation?

    Thanks in advance.

    Sincerely,
    Niles.
     
  2. jcsd
  3. Dec 26, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Well, the obvious first step is to cancel the "A"s: [itex]cos(\omega t)e^{-Ct}= 1/2[/itex]. Next, I think I would write the cosine in exponential form: [itex]cos(\omega t)= (e^{it}+ e^{-it})/2[/itex] so [itex]cos(\omega t)e^{-Ct}= (e^{(-C+ i\omega)t}+ e^{(C-i\omega)t})2= 1/2[/itex]
     
  4. Dec 27, 2008 #3
    Ahh, great.

    If I was given a function on the form:

    [tex]
    V(t)=(A\cos(\omega t)+B\sin(\omega t)\exp(-Ct),
    [/tex]

    then writing the sines and cosines as exponentials would be the way to go too. But am I even correct to say that the time t when the amplitude of the oscillation of V(t) is half of the original amplitude is when V(t) = A/2, where A is the amplitude?
     
    Last edited: Dec 27, 2008
  5. Dec 27, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, you said "find the time find the time t, where the amplitude is A/2". If the initial amplitude is A, then half of it is A/2.
     
  6. Dec 27, 2008 #5
    Need numerical solve.
     
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