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The time-varying response of the Earth's and other planets' rotation toexternal gravitational torques depends strongly on their internal structure. Inparticular, the existence of the mode known as the Free Core Nutation in thefluid core, is known to amplify the forced nutations in the near-diurnalretrograde frequency band (as measured in the planetary frame of reference).Due to their proximity in shape and frequency, this mode is sometimes equatedwith the so-called Spin-Over Mode which denotes the free oscillation of asteadily rotating ellipsoidal fluid core. Through a careful study of the freelyrotating two-layer planetary model with a rigid mantle and an inviscid fluidcore, we show that the Spin-Over Mode frequency corresponds to that where thesum of the external and internal torques on the mantle are balanced, causing itto rotate steadily. The presence of dissipation at the Core-Mantle Boundarycauses the Free Core Nutation to become damped and slightly offset itsresonance frequency. We show that this offset, which is $\approx-1$ day for theEarth, can be interpreted as the result of the proximity of the Free CoreNutation frequency to that of the Spin-Over Mode, which now corresponds to aminimum in the magnitude of the transfer function for nutations. We also showhow this proximity leads to a slightly lower Quality factor for the resonancethan that compute from the usual formula. We conclude by discussing possibleimplications of this mechanism for Mars, the Moon, and the long-term evolutionof the Earth.

Free Core Nutation and its relation to the Spin-Over Mode