The query is in English, so the output should be English too.

Free and forced vibrations differ primarily in their causes and characteristics within vibration analysis.

Key Insights

• Free Vibration:

  • Definition: Occurs when a system oscillates due to an initial disturbance and continues without external forces acting on it.
  • Characteristics: The system vibrates at its natural frequency, and the amplitude gradually decreases over time due to damping.
  • Examples: A plucked guitar string, a swinging pendulum after being released.

• Forced Vibration:

  • Definition: Occurs when a system is continuously driven by an external force.
  • Characteristics: The system vibrates at the frequency of the external force, which may differ from its natural frequency. The amplitude can increase if the driving frequency is close to the system's natural frequency, potentially leading to resonance.
  • Examples: A building shaking due to an earthquake, machinery vibrating due to motor operation.

Conclusion

Free vibration is characterized by natural frequency oscillations without external forces, while forced vibration involves continuous external driving forces, potentially leading to resonance if the driving frequency matches the system's natural frequency.