The oscillations are not "around" the plane, they are through the plane. That is; the plane itself has a local gravitational attraction which is orthogonal to

The oscillations are not "around" the plane, they are through the plane. That is; the plane itself has a local gravitational attraction which is orthogonal to the galaxy core gravitational attraction. If a mass is above or below the plane, the "local" gravity will pull towards the plane. since nothing stops it at the mid line of the plane it passes through to the opposite side; rinse and repeat. This bouncing above and below center line of the disk is more or less independent of our solar system completing galactic orbits.