Sliding Down a Helix

A bead slides from rest down a wire that's bent into a helix, which can be parametrized in the following way: \[ \begin{cases} x = \cos(\theta) \\ y = \sin(\theta) \\ z = \theta. \end{cases} \] Find the magnitude of the bead's vertical acceleration.

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Assumptions: The bead slides without friction and there is a uniform, gravitational field \(-g\,\hat{\mathbf{z}}.\)

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