Define forced and resonant vibrations

Answer

### Step-by-Step Solution:

1. **Definition of Forced Vibrations**:
- Forced vibrations occur when an external periodic force is applied to a system. This force has a frequency that is different from the natural frequency of the system.
- In this case, the body continues to oscillate due to the influence of this external force, regardless of its natural tendency to oscillate at its own frequency.

2. **Characteristics of Forced Vibrations**:
- The amplitude of forced vibrations can vary depending on the strength of the external force and the frequency of that force.
- If the frequency of the external force is close to the natural frequency of the system, the amplitude of the oscillation can increase significantly.

3. **Definition of Resonant Vibrations**:
- Resonant vibrations occur when the frequency of the external force matches the natural frequency of the system.
- At this point, the system can oscillate with maximum amplitude because the energy input from the external force is perfectly in sync with the system's natural oscillation.

4. **Characteristics of Resonant Vibrations**:
- Resonance can lead to large oscillations and can sometimes cause structural failure if the amplitude becomes too great.
- This phenomenon is commonly observed in musical instruments, bridges, and buildings.

### Summary:
- **Forced Vibrations**: Oscillations maintained by an external periodic force with a frequency different from the natural frequency of the body.
- **Resonant Vibrations**: Oscillations that occur when the external force frequency matches the natural frequency of the system, resulting in maximum amplitude.

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