Quality factor via energy loss

The quality factor of the system can be defined using the energy stored in the system and the power dissipated from the system. In electrical system, the loss of energy occurs due to resistors; in mechanical systems, it occurs due to external forces.

Notes:

1. There is another definition that is approximately equivalent to this one at high quality factor values.

Links:

1. Wikipedia.

quality_factor

quality_factor of the oscillator.

Symbol:

Q

Latex:

\(Q\)

Dimension:

dimensionless

resonant_angular_frequency

Resonant angular_frequency of the oscillator.

Symbol:

w_r

Latex:

\(\omega_\text{r}\)

Dimension:

angle/time

energy_stored

energy stored in the oscillator.

Symbol:

E_stored

Latex:

\(E_\text{stored}\)

Dimension:

energy

power_loss

power lost by the oscillator, i.e. the rate of energy dissipating from it.

Symbol:

P_loss

Latex:

\(P_\text{loss}\)

Dimension:

power

law

Q = w_r * E_stored / P_loss

Latex:

\[Q = \omega_\text{r} \frac{E_\text{stored}}{P_\text{loss}}\]