Damping opposes oscillations. It is caused by the resistance of the fluid in which the oscillations take place. There are three types of damping:

• Under-damping - in which the body continues to oscillate with decreasing amplitude (may be light or heavy)
• Critical damping - in which the body returns to its equilibrium position in the shortest possible time without over-shooting
• Over-damping - in which the body returns to its equilibrium position slowly without over-shooting

In under-damped systems, the amplitude decreases according to an exponential decay relationship.

The Q (quality) factor for oscillations is a dimensionless quantity that indicates the extent of damping. It is calculated as follows:

\(Q=2\pi {\text{energy stored}\over \text{energy dissipated per cycle}}\)

• \(Q\) is the Q factor (dimensionless)
• The energy stored is the energy at the beginning of a cycle (J)
• The energy dissipated per cycle is the energy lost in the system as a result of that same cycle (J)

Critical damping occurs when \(Q={1\over 2}\). A system with \(Q>{1\over 2}\) is under-damped and a system with \(Q<{1\over 2}\) is over-damped.

Since the energy dissipated in one cycle is equal to the power loss multiplied by the time for that cycle:

\(Q=2\pi \times {\text{energy stored}\over \text{power loss}\times T}\)

\(\Rightarrow Q=2\pi \times \text{resonant frequency}\times {\text{energy stored}\over \text{power loss}}\)

• \(Q\) is the Q factor (dimensionless)
• The resonant frequency is the frequency of the oscillations (Hz)
• The energy stored is the energy at the beginning of a cycle (J)
• The power loss is the energy lost per unit time during that same cycle (W)