An oscillation is damped when an external force that acts on the oscillator has the effect of decreasing the amplitude of its oscillations. 

  1. Light damping causes the amplitude of the oscillator to gradually decrease with time. The period is unchanged.
  2. Heavy damping causes the amplitude to decrease quickly and significantly. The period of the oscillations also increase slightly.
  3. Critical damping causes the oscillator to return to its equilibrium position in the minimum amount if time (very heavy damping – unlikely to overshoot).

In all cases of damped motion, the kinetic energy of the oscillator is transferred to other forms (usually heat).

When a mechanical system is displaced from its equilibrium position and then allowed to oscillate without any external forces, its motion is referred to as free oscillation. The frequency of free oscillations is the natural frequency of the oscillator. A forced oscillation is where a periodic driver force is applied to an oscillator, causing it to vibrate at the driving frequency. If the driving frequency is equal to the natural frequency, resonance occurs and the amplitude of the system increases greatly. 

For a forced oscillator with negligible damping, at resonance

driving frequency = natural frequency of the forced oscillator

When an object resonates, the amplitude of the oscillation increases considerably. If the system is not damped, the amplitude will increase to the point at which the object fails. The greatest possible transfer of energy from the driver to the forced oscillator occurs at the resonant frequency. 

Practical examples of forced oscillators and resonance:

  1. Clocks (use a pendulum or quartz crystal)
  2. Musical instruments
  3. Tuning circuits
  1. For light damping the maximum amplitude occurs at the natural frequency of the forced oscillator. As the amount of damping increases:Magnetic resonance imaging
  1. The amplitude of vibration at any frequency decreases
  2. The maximum amplitude occurs at a lower frequency

3. The peak on the graph becomes flatter and broader