Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Section B / 8 / d

The starting radius is $r_0=\sqrt{2}c$. In uniform circular motion, the required centripetal acceleration has magnitude ${\omega }^2{r}_0=k{r}_0/m$. The initial velocity must be tangent to the starting radius, with the orientation chosen anticlockwise:The resulting trajectory isIt has constant $x^2+y^2=2c^2$, soThis is the horizontal line in the right panel of the figure. The kinetic energy also equals $k{c}^2$, giving total mechanical energy $2k{c}^2$, twice that for release from rest at the same point.