When the frequency of an oscillator is slightly greater than that of resonance, the effect on the amplitude of the oscillator depends on the damping present in the system. Let's consider two scenarios:
Underdamped System: In an underdamped system, where there is relatively low damping, when the frequency of the oscillator is slightly greater than the resonance frequency, the amplitude of the oscillator will gradually decrease over time. This effect is known as "decay" or "attenuation." The amplitude will decrease because the frequency of the driving force is not precisely matching the natural frequency of the system, resulting in a phase difference between them. As time progresses, this phase difference causes the amplitude to decrease.
Overdamped or Critically Damped System: In an overdamped or critically damped system, where there is high damping, the effect of a slightly higher frequency than resonance is less pronounced. In these cases, the system does not exhibit resonance behavior, and the amplitude does not experience significant changes. The system will return to its equilibrium position without oscillating.
It's important to note that the effect on the amplitude may also depend on the specific characteristics and parameters of the oscillator system, such as the amount of damping, the quality factor (Q-factor), and the exact difference between the frequency and resonance frequency.