Question

Explain what do we mean by free,forced and resonant vibrations

Answer 1

Forced Vibrations & Resonance. Free vibrations are oscillations where the total energy stays the same over time. This means that the amplitude of the vibration stays the same. ... Forced vibrations occur when the object is forced to vibrate at a particular frequency by a periodic input of force.

This is an example of resonance - when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. The result of resonance is always a large vibration. Regardless of the vibrating system, if resonance occurs, a large vibration results.

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Answer 2

Free vibrations are oscillations where the total energy stays the same over time. This means that the amplitude of the vibration stays the same. This is a theoretical idea because in real systems the energy is dissipated to the surroundings over time and the amplitude decays away to zero, this dissipation of energy is called damping.

Free vibration

Light damping

Heavy damping

Critical damping

Overdamped

 Forced vibrations occur when the object is forced to vibrate at a particular frequency by a periodic input of force.

Objects which are free to vibrate will have one or more natural frequencyat which they vibrate,

If an object is being forced to vibrate at its natural frequency, resonancewill occur and you will observe large amplitude vibrations. The resonant frequency is fo.

Effect of damping on resonance graph.

The amplitude of the resonance peak decreases and the peak occurs at a lower frequency.

Phase and resonance

The phase relationship between the driving oscillation and the the oscillation of the object being driven is different at different frequencies.

Below resonance they are in phase with each other.At resonance the phase relationship is 90o or p/2 rad.Above resonance the phase relationship is 180o or p rad.