The kinetic energy $T$ is given by $T = \frac{1}{2} m v^2$, where $v$ is the velocity of the mass $m$. In cylindrical coordinates, the velocity squared $v^2$ is given by $v^2 = \dot{r}^2 + r^2 \dot{\theta}^2 + \dot{z}^2$. Therefore, the kinetic energy is
\[T =
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