Displacement in simple harmonic motion
======================================

Any motion that repeats at regular intervals is called periodic, or harmonic, motion.
Simple harmonic motion is a particular type of repeated motion that is a sinusoidal
function of time.

**Note:**

#. This law is also applicable for any physical quantity that changes its value in
   a repeating harmonic manner, therefore :attr:`~symplyphysics.symbols.basic.any_quantity` is used.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics>`__.

.. py:currentmodule:: symplyphysics.laws.kinematics.displacement_in_simple_harmonic_motion

.. py:data:: displacement

    Displacement from rest, usually a function of :attr:`~symplyphysics.symbols.basic.time`. See :attr:`~symplyphysics.symbols.basic.any_quantity`.

Symbol:
    :code:`q`

Latex:
    :math:`q`

Dimension:
    :code:`any_dimension`


.. py:data:: amplitude

    The maximum absolute value of the :attr:`~displacement`. See :attr:`~symplyphysics.symbols.basic.any_quantity`.

Symbol:
    :code:`q_max`

Latex:
    :math:`q_\text{max}`

Dimension:
    :code:`any_dimension`


.. py:data:: angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of oscillations.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: phase_shift

    :attr:`~symplyphysics.symbols.classical_mechanics.phase_shift` of oscillations, which is the phase at :math:`t = 0`.

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time` at which :attr:`~displacement` is measured.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`q = q_max * cos(w * t + phi)`


    Latex:
        .. math::
            q = q_\text{max} \cos{\left(\omega t + \varphi \right)}