Quality factor via damping ratio
================================

In case of a damped oscillating system where the damping force is linearly proportional
to the oscillator's frequency, the :math:`Q` factor of the oscillator is inversely
proportional to the system's damping ratio. Hence greater values of the :math:`Q` factor
correspond to lower values of the damping ratio and to lower damping.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Damping#Q_factor_and_decay_rate>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.damped_oscillations.quality_factor_via_damping_ratio

.. py:data:: quality_factor

    :attr:`~symplyphysics.symbols.classical_mechanics.quality_factor` of the oscillator.

Symbol:
    :code:`Q`

Latex:
    :math:`Q`

Dimension:
    :code:`dimensionless`


.. py:data:: damping_ratio

    :attr:`~symplyphysics.symbols.classical_mechanics.damping_ratio` of the oscillator. Also see :ref:`Damped harmonic oscillator equation`.

Symbol:
    :code:`zeta`

Latex:
    :math:`\zeta`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`Q = 1 / (2 * zeta)`


    Latex:
        .. math::
            Q = \frac{1}{2 \zeta}