AbstractBy transforming a 1D second‐order linear oscillator into a 2D first‐order polar motion differential equation, it can be shown that the finite smoothness (i.e., the presence of jump in finite order derivatives) of the applied Newtonian forcing constitutes the sufficient and necessary condition for instantaneous excitation of free eigen‐mode. This condition can be met by forcing functions originated from turbulent and multiphase fluid motions. Sub‐macroscopic transition time associated with astatic elastic deformation limits the physical smoothness of the applied forcing for the Earth's polar motion. Eigen‐modes can also be excited by an infinitely smooth forcing that has a finite domain of non‐zero values. The eigen‐period serves as a macroscopic timescale to characterize the inertia of a linear oscillator. If a zero mean irregular forcing of finite smoothness exhibits a high degree of randomness and the timescale is much shorter than the eigen‐period, then for negligible damping the eigen‐waveform will increase in proportion to the squareroot of time, while the waveform distortion is statistically a constant. As a result, the pattern of distinctive eigen‐oscillation will dominate the forced solution for longer enough duration.