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Equation for underdamped harmonic motion

  1. Jan 24, 2016 #1
    I found an explanation for the equation of under damped harmonic motion, x(t) = C cos(wt) + D sin(wt), but I was wondering if someone could further explain why:

    - "However, if you assume the function x(t) is real, then they are related as A = B
    - why is (A-B) is imaginary
     

    Attached Files:

  2. jcsd
  3. Jan 24, 2016 #2
    If A and B are conjugates, A = (g,h) and B = (g,-h).

    A + B = (g,h) + (g,-h) = (2g,0). This is a real number.
    A - B = (g,h) - (g,-h) = (0,2h). This is a complex number.
     
  4. Jan 24, 2016 #3
    thanks,
    can you also explain the "However, if you assume the function x(t) is real, then they are related as A = B" bit
     
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