Forced vibration and free vibration are two types of vibrational behaviors exhibited by systems. Here's an explanation of the differences and their effects:
Free Vibration: Free vibration occurs when a system oscillates on its own after being given an initial disturbance or displacement. In free vibration, the system has no external force acting on it. The amplitude and frequency of free vibration depend on the system's natural frequency and damping characteristics. The system will vibrate at its natural frequency and gradually lose energy over time due to internal or external damping. The phase angle at resonance for free vibration is typically 0°.
Forced Vibration: Forced vibration occurs when an external force is applied to a system, causing it to vibrate. The external force may be periodic or non-periodic and can be continuous or intermittent. In forced vibration, the system is driven by an external force, such as an applied oscillatory motion or an input signal. The amplitude and frequency response in forced vibration depend on the characteristics of the driving force and the system's dynamics. If the driving force frequency matches the natural frequency of the system, resonance can occur, resulting in a significant increase in the amplitude of the vibration. The phase angle at resonance for forced vibration is typically 180°.
Effects on Amplitude and Frequency Response:
Free Vibration: In free vibration, the amplitude of the vibration gradually decreases over time due to damping effects. The natural frequency of the system determines the frequency of the vibration, and the amplitude decreases exponentially over successive oscillations.
Forced Vibration: In forced vibration, the amplitude of the vibration depends on the characteristics of the driving force. If the driving force frequency matches the natural frequency of the system, resonance can occur, leading to a significant increase in amplitude. For frequencies away from resonance, the amplitude remains relatively smaller. The frequency response of the system in forced vibration is influenced by the driving force frequency and the system's dynamics.
Phase Angle at Resonance:
Free Vibration: The phase angle at resonance for free vibration is typically 0°. This means that the displacement and the driving force are in phase with each other.
Forced Vibration: The phase angle at resonance for forced vibration is typically 180°. This means that the displacement and the driving force are exactly out of phase with each other.
In summary, free vibration occurs naturally without any external force, while forced vibration is driven by an external force. Free vibration gradually loses energy over time, while forced vibration can exhibit resonance at the system's natural frequency. At resonance, forced vibration results in a significant increase in amplitude, while in free vibration, the amplitude gradually decreases. The phase angle at resonance is 0° for free vibration and 180° for forced vibration.