Why Does the System Have a Zero Frequency in the Normal Mode Oscillations?

[deadringer]

Homework Statement

Two equal masses are connected by two massless springs of constant k and nat. length l. The masses are constrained by a frictionless tube on a pivot, (also massless) so that they remain colinear with the pivot. The pivot subtends angle theta with the vertical. The 1st mass is at distance r1 from the pivot (therefore the 1st spring has length r1) and the second mass is at r2 from the pivot.
We need to find the normal mode frequencies of oscillation about stable equil.

Homework Equations

The Attempt at a Solution

I have found the Lagrangian, equations of motion, equilibrium point and normal mode frequencies. The only problem is that I get one frequency of zero, and I don't understand physically what is going on (this is not an oscillating solution but a constant solution). This appears to imply that the system is displaced from equilibrium and just stays at the new position (i.d does not oscillate about equil. or diverge from equil.), although physically this seems not to make sense.

 

[berkeman]

I would think that the zero frequency solution is just for when there is no initial displacement.

 

[christianjb]

The zero frequency comes from displacement of the center of mass.
In 3D you get 6 zero frequencies corresponding to 3 displacements of the C.O.M and 3 rotations about the C.O.M.