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I Mechanical energy in an harmonic wave and in normal modes

  1. May 20, 2016 #1
    I think I miss something about energy of a mechanical wave.
    In absence of dissipation the mechanical energy transported by an harmonic wave is constant.

    $$E=\frac{1}{2} A^2 \omega^2 m$$

    But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still constant) is equal to

    $$E=\frac{1}{4} A^2 \omega^2 m$$

    Is the factor ##\frac{1}{2}## really present and why?
     
  2. jcsd
  3. May 20, 2016 #2
    Are you sure the first formula is about a wave? What would be the meaning of m?
    Isn't the energy of a harmonic oscillator?
     
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