Damped angular frequency
========================

A damped oscillator performs oscillations with a frequency proportional
to that of an undamped oscillator, i.e. to the frequency of an oscillator when
there is no damping force acting on the system.

**Notes:**

#. In the case of overdamping when the damping ratio is greater than 1, the value of damped
   angular frequency becomes imaginary, which indicates the absence of oscillations.

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

.. py:data:: damped_angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of a damped oscillator.

Symbol:
    :code:`w_d`

Latex:
    :math:`\omega_\text{d}`

Dimension:
    :code:`angle/time`


.. py:data:: undamped_angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of an undamped oscillator.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. 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:: law

    :code:`w_d = w * sqrt(1 - zeta^2)`


    Latex:
        .. math::
            \omega_\text{d} = \omega \sqrt{1 - \zeta^{2}}