Rotating disks

Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $\omega$ . The discs are in the same horizontal plane. At time $t = 0$ , the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_r$ . In one time period $(T)$ of rotation of the discs, $v_r$ as a function of time is best represented by