Electrified Bow and Arrow

We consider an electrostatic bow and arrow both charged positively. The bow is circular and horizontal the massive arrow is vertically aligned with the bow’s symmetry axis with its head up. The arrow is released freely, the electrically charged ring repels the arrow and the gravity slows its uprise. The mass, length, and charge of the arrow as well as the size of the ring and its charge adjusted making the arrow oscillate up and down. The kinematic and dynamic quantities of the oscillations are calculated, and the relevant phase diagrams are depicted. In pursuing these goals, a Computer Algebra System (CAS) specifically Mathematica [1] is used. Among various scenarios, the case of a charged ring and a point charge is discussed.