n=2, L=m(l)=0 should be correct for the reasons you have outlined above.
If you are being asked for the corresponding Set(!) of quantum numbers I believe you want to include both the spin-up and spin-down states in your answer.
Derive the equations of motion for three identical pendula A, B and C, of mass m and length L coupled together (A to B and B to C) with two identical springs of low spring constant k.
Can't quite appreciate the forces acting on these pendula as they all should be...