Period of spring from mass
==========================

Mass on spring is a system of object with mass :math:`m` and spring with stiffness :math:`k`.
It starts oscillating after being pushed out of balance.

**Conditions:**

#. The spring does not gain or lose energy. There is no friction or inelastic deformation.
#. The object is small enough to be considered a material point.
#. The spring is weightless.

**Links:**

#. `Wikipedia, second formula <https://en.wikipedia.org/wiki/Spring_(device)#Frequency_&_period>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.period_of_spring_from_mass

.. py:data:: period

    The :attr:`~symplyphysics.symbols.basic.period` of spring oscillations.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`time`


.. py:data:: mass

    The :attr:`~symplyphysics.symbols.basic.mass` of the object attached to the spring.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: stiffness

    Spring's :attr:`~symplyphysics.symbols.classical_mechanics.stiffness`, or spring constant.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`force/length`


.. py:data:: law

    :code:`T = 2 * pi * sqrt(m / k)`


    Latex:
        .. math::
            T = 2 \pi \sqrt{\frac{m}{k}}