Period of ideal pendulum from length
====================================

An ideal pendulum is an object hanging on a thread. In a gravitational field it starts oscillating after being pushed out of balance.
Period of pendulum oscillation does not depend on its mass.

**Conditions:**

#. The angle between pendulum and gravity vector is fairly small (less than 15 degrees).
#. Ideal pendulum doesn't gain or lose any energy, so there is no friction in the system.
#. The object is small enough to be considered a material point.
#. The thread is weightless and doesn't change its length.

**Links:**

#. `Wikipedia, first formula <https://en.wikipedia.org/wiki/Pendulum#Period_of_oscillation>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.period_of_ideal_pendulum_from_length

.. py:data:: period

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`time`


.. py:data:: length

    The :attr:`~symplyphysics.symbols.classical_mechanics.length` of the pendulum.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`T = 2 * pi * sqrt(l / g)`


    Latex:
        .. math::
            T = 2 \pi \sqrt{\frac{l}{g}}