Damping ratio from decay constant and undamped frequency
========================================================

The damping ratio of an oscillator can be calculated via the exponential decay constant,
which describes how fast its oscillations decay, and its undamped angular frequency.

.. py:currentmodule:: symplyphysics.laws.kinematics.damped_oscillations.damping_ratio_from_decay_constant_and_undamped_frequency

.. py:data:: damping_ratio

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

Symbol:
    :code:`zeta`

Latex:
    :math:`\zeta`

Dimension:
    :code:`dimensionless`


.. py:data:: exponential_decay_constant

    :attr:`~symplyphysics.symbols.basic.exponential_decay_constant` of the oscillator.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`1/time`


.. py:data:: undamped_angular_frequency

    Undamped :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the oscillator.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: law

    :code:`zeta = lambda / w`


    Latex:
        .. math::
            \zeta = \frac{\lambda}{\omega}