If we have a driven damped harmonic oscillator: $$ \frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega^2_0x=\frac{F}{m} e^{i\omega t} $$
amplitude resonant frequency occurs at: $ \omega_R^2 = \omega^2_0x-\frac{\gamma^2}{2} $ As energy of a spring is proportional to displacement squared, the maximum energy of the system is here.
But, velocity resonance occurs at: $\omega=\omega_0$ as kinetic energy is proportional to velocity squared, the maximum energy of the system is here.
There is clearly a paradox here, I cannot understand how it can resonate at 2 different frequencies.