.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/mechanical_engineering/plot_mechanical_engineering_benchmark.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_mechanical_engineering_plot_mechanical_engineering_benchmark.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_mechanical_engineering_plot_mechanical_engineering_benchmark.py:


Oscillator energy balance
=========================

An unforced undamped oscillator conserves kinetic plus spring energy.
Viscous damping removes that energy; compare both against the initial value.

.. GENERATED FROM PYTHON SOURCE LINES 8-28



.. image-sg:: /api/gallery/mechanical_engineering/images/sphx_glr_plot_mechanical_engineering_benchmark_001.png
   :alt: plot mechanical engineering benchmark
   :srcset: /api/gallery/mechanical_engineering/images/sphx_glr_plot_mechanical_engineering_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.mechanical_engineering import simulate_sdof

    t = np.linspace(0, 10, 501)
    fig, ax = plt.subplots()
    for c in [0, 0.4]:
        result = simulate_sdof(1, c, 4, x0=0.1, t=t)
        E = 0.5 * result.velocity**2 + 2 * result.displacement**2
        if c == 0:
            np.testing.assert_allclose(E, 0.02, rtol=1e-5)
        else:
            assert E[-1] < E[0]
        ax.plot(t, E, label=f"c={c} N s/m")
    ax.set(xlabel="time [s]", ylabel="mechanical energy [J]")
    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.133 seconds)


.. _sphx_glr_download_api_gallery_mechanical_engineering_plot_mechanical_engineering_benchmark.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/mechanical_engineering/plot_mechanical_engineering_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_mechanical_engineering_benchmark.ipynb <plot_mechanical_engineering_benchmark.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_mechanical_engineering_benchmark.py <plot_mechanical_engineering_benchmark.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_mechanical_engineering_benchmark.zip <plot_mechanical_engineering_benchmark.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_