Sketching a Graph of a Particle Trajectory

Question

How can I sketch the trajectory of a particle of mass $m$ with a position vector

$\mathbf{r} = \cos(\omega t)\,\hat{\mathbf{i}} + \sin(3\omega t)\,\hat{\mathbf{j}}$ ?

Will this be a three dimensional graph, with an $x, y, t$ coordinate system?

Answer 1

This will be a 2-dimensional graph, since the position vector r has 2 components.

Draw an x,y plane. At time t, the x position is $\cos(\omega t)$ and the y position is $\sin(3\omega t)$.