= Solution
The disk still has only \b[three degrees of freedom and hence three normal modes]: two centre coordinates and one in-plane rotation. Five springs alter the restoring <quadratic form> but add no disk coordinates. The fivefold <rotational symmetry> makes the translational stiffness proportional to the two-dimensional <identity matrix>, and makes translation-rotation coupling vanish. Therefore \b[the two translation modes are always degenerate]; the rotational mode is separate, with possible accidental equality of its frequency for particular parameters. The general formulas in <small oscillations of a disk attached to prestretched radial springs> apply with $N=5$.
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