Define the curvature, $\kappa$, of a curve in $\mathbb{R}^{3}$.

The curve $C$ is parametrised by

$$\mathbf{x}(t)=\left(\frac{1}{2} e^{t} \cos t, \frac{1}{2} e^{t} \sin t, \frac{1}{\sqrt{2}} e^{t}\right) \quad \text { for }-\infty<t<\infty$$

Obtain a parametrisation of the curve in terms of its arc length, $s$, measured from the origin. Hence obtain its curvature, $\kappa(s)$, as a function of $s$.