**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 frequency** at which they vibrate,

If an object is being forced to vibrate at its natural frequency, **resonance **will occur and you will observe large amplitude vibrations. The resonant frequency is f_{o}.

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 90
^{o}or p/2 rad. - Above resonance the phase relationship is 180
^{o}or p rad.

Click this link to see MIT video on a ‘Driven Mechanical Oscillator’

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