This is the equation for a $2$D damped sine wave, what is the $3$D equivalent?
For reference, a $2$D sine wave would be of form $y=\sin x$, and a 3D sine wave would be of form $z=\sin(\sqrt{x^2 + y^2})$.
The $3$D equation for a damped sine wave
trigonometrywave equation
Related Solutions
Try the following, where $t$ represents the main parameter, $\theta$ is the tilting angle as the sine wave wraps around the cylinder, $k$ is the frequency of the sine wave, and $a$ is the amplitude:
$$\begin{align*} x(t) &= \cos (t \cos \theta - a \sin \theta \sin (k t)) \\ y(t) &= \sin (t \cos \theta - a \sin \theta \sin (k t)), \\ z(t) &= t \sin \theta + a \cos \theta \sin (k t). \end{align*}$$
Fancy animated picture! 
How about $$ f(x) = \frac{1}{2}\left(\sin(x) + \left| \sin{x} \right| \right) $$
Best Answer
As in the comments, the equation
$$z=e^{-\sqrt{x^2+y^2}}\sin(\sqrt{x^2+y^2})$$ or else phase-shifted and scaled as $$z=e^{-\sqrt{x^2+y^2}}\cos(2\pi\sqrt{x^2+y^2})$$
expresses damping along any ray $ax+by=0$ extending from the origin, and this was achieved by substitution of $\sqrt{x^2+y^2}$ in place of $t$ in the Wikipedia listing at https://en.m.wikipedia.org/wiki/Damped_sine_wave.