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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?