Final answer:
The natural frequency to forcing frequency ratio for in-phase motion is ideally 1:1, indicating that both frequencies are equal and the system resonates with the maximum amplitude when there is minimal damping.
Step-by-step explanation:
The natural frequency to forcing frequency ratio for in-phase motion refers to a specific condition in the context of forced oscillations and resonance in a harmonic oscillator. When a system is subjected to a periodic force that matches its natural frequency, the force is said to be in resonance with the system, and the motion will be in-phase with the driving force, resulting in a resonant peak in amplitude. The ratio of natural frequency (f) to forcing frequency (ω) for in-phase motion is ideally 1:1, signifying that the two frequencies are equal and the system will resonate, maintaining a constant phase relationship with the driving force. This condition is achieved when there is minimal or no damping present in the system, allowing for the maximum energy transfer and thus maximum oscillation amplitude at the resonant frequency.