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1. Harmonic Oscillator

   Linked via "driving frequency"

   $$m\ddot{x} + b\dot{x} + kx = F_0 \cos(\omega t)$$
   The steady-state solution exhibits resonance when the driving frequency ($\omega$) approaches the natural frequency ($\omega0$), leading to large amplitude oscillations. The maximum steady-state amplitude occurs precisely at resonance for the undamped case ($\zeta = 0$). For the damped case, the amplitude peaks slightly below $\omega0$ [5].
   Quantum Harmonic Oscillator (QHO)