Aparticle of mass m moves in a singular central potential with v(r) = with > -lambda r^-n with n > 2. reduce the equations of motion to an equivalent one-dimensional problem and discuss the qualitative nature of the orbit for different values of the energy. for the bound orbits, show that the particle takes a finite length of time to spiral into the center of force, passing through a finite number of revolutions. can you say anything about the subsequent motion?