8.1.4.1 Geometric and physical applications

Problem: A material point of mass \( \mathrm{m} \) is attracted by the center \( O \) with a force, proportional to the distance. The movement starts from point \( A \) at a distance \( a \) from the center with an initial speed \( v_{0} \), perpendicular to the segment \( O A \). Find the trajectory of motion.