"Harumodoki (春擬き, Pseudo-Spring)" is the opening song for season 2. There are 2 different videos of the OP. The first version is used in episodes 1-2, and the second version is used in 3-13 and OVA Zoku.
It is sung by Nagi Yanagi and included in the "Follow My Tracks" album (not related to OreGairu).
The video may or may not work. It is often taken down due to copyright claims.