I Mechanical energy in an harmonic wave and in normal modes

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1. May 20, 2016

crick

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. May 20, 2016

nasu

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?