And how exactly do objects acquire "natural frequencies"? Is it due to the temperature and the lattice structure (the type of bonds they form with other atoms)? And thus, is resonance just a phenomenon that preserves energy within the lattice than leak it outside?
And is the below illustration accurate for explaining resonance?
Case 1: A hollow metal sphere. Say its natural frequency is 20 Hz. So, if we hit it with a hammer and the resultant energy (by accident/chance) makes it vibrate at 20 Hz, then it takes $n$ seconds to cool down and loses $x$ Joules to the atmosphere as heat energy (per second).
Case 2: Same sphere as above. We hit it with another hammer but more forcibly. It vibrates at 22 Hz in the beginning, and because that's not its natural frequency, it comes to a standstill at $n+4$ seconds, losing $x+4$ Joules as heat energy in the process (per second).
Case 3: Same sphere as above. We hit it with a smaller hammer, lightly. It initially vibrates at 18 Hz. Since that's also not the right frequency as the natural one, it loses energy fast but not as fast as Case 1, as the total energy, in this case, is also low (Law of Equilibrium says that one side has too much energy, it loses energy fast to reach the equilibrium). Say it takes $n+2$ seconds and loses $x+2$ energy per second.
What if we increase the impact in Case 1 by a thousand times (assuming the object doesn't break)? Will the resonant frequency still last longer than the frequency generated by the impact? Is there a threshold that tells the exact amount of energy that is required to cross this resonant threshold of losing energy?