9.6 Exercise 9

Two particles of masses $m_{1}$ and $m_{2}$ move uniformly in different circles of radii $R_{1}$ and$R_{2}$ about the origin in the x, y-plane. The coordinates of the two particles in meters are given as follows ($z = 0$ for both). Here t is in seconds:
$\begin{aligned}x_{1} \left(t\right) & = & 4 \text{cos} \left(2 t\right) \\ y_{1} \left(t\right) & = & 4 \text{sin} \left(2 t\right) \\ x_{2} \left(t\right) & = & 2 \text{cos} \left(3 t - \frac{\pi}{2}\right) \\ y_{2} \left(t\right) & = & 2 \text{sin} \left(3 t - \frac{\pi}{2}\right)\end{aligned}$

1. Find the radii of the circles of motion of both particles.
2. Find the x- and y-coordinates of the center of mass.
3. Decide if the center of mass moves in a circle by plotting its trajectory.