Physics/A/String vibration/Energy (advanced)

Template:String vibration energy density using Rowland's notation:

$u={\tau }_0({\xi }^{\prime }+\frac{1}{2}\eta {\text{'}}^2)$

If $\ell =1$, I think I get:

$u={\kappa }_T({\xi }^{\prime }+\frac{1}{2}\eta {\text{'}}^2)$