Final answer:
The largest amplitude of an oscillator with a sinusoidal force applied is achieved when the frequency of the applied force equals the oscillator's natural frequency, known as resonance, particularly with the least amount of damping.
Step-by-step explanation:
To obtain the largest possible amplitude of an oscillator when a sinusoidal force is applied, the oscillation frequency of the applied force should be equal to the natural frequency of the oscillator. This phenomenon is known as resonance, which leads to the maximum amplitude response (Amax) in a given system with damping forces present. Less damping results in a higher amplitude because less energy is removed by the damping force at resonance.
Figures specifically cite that resonance occurs when the driving frequency equals the natural frequency, resulting in the greatest response for the least amount of damping. As shown in the amplitude response graphs, the peak of each curve, representing different damping levels, aligns with the system's natural frequency, demonstrating that this is the point at which the amplitude reaches its maximum value.