[QUE/ME-12002]

Consider  a particle of mass \(\mu\) moving in a potential \[ V(r) = \frac{1}{2}\mu\omega^2 r^2  +\frac{\lambda^2}{2\mu r^2}. \] Does there exist a circular orbit for \(L=0\)? Assume  \(L=0, E= \frac{25}{2}\mu\omega^2a^2\), \(\lambda=12\mu\omega^2\) Use initial conditions \[ r(t)\big|_{t=0} = 4a;\quad \dot{r}(t)\big|_{t=0} = 0   \text{ and } \dot{\theta(t)}\big|_{t=0}=0 \] solve the equations of motion and obtain \(r\), \(\theta\) as function of time. Describe the motion that takes place under conditions specified here.

AKK