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

    Click :ref:`here <sphx_glr_download_intro_scipy_auto_examples_plot_odeint_damped_spring_mass.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_scipy_auto_examples_plot_odeint_damped_spring_mass.py:


============================================
Integrate the Damped spring-mass oscillator
============================================






.. image:: /intro/scipy/auto_examples/images/sphx_glr_plot_odeint_damped_spring_mass_001.png
    :class: sphx-glr-single-img





.. code-block:: python


    import numpy as np
    from scipy.integrate import odeint
    from matplotlib import pyplot as plt

    mass = 0.5  # kg
    kspring = 4  # N/m
    cviscous = 0.4  # N s/m


    eps = cviscous / (2 * mass * np.sqrt(kspring/mass))
    omega = np.sqrt(kspring / mass)


    def calc_deri(yvec, time, eps, omega):
        return (yvec[1], -eps * omega * yvec[1] - omega **2 * yvec[0])

    time_vec = np.linspace(0, 10, 100)
    yinit = (1, 0)
    yarr = odeint(calc_deri, yinit, time_vec, args=(eps, omega))

    plt.figure(figsize=(4, 3))
    plt.plot(time_vec, yarr[:, 0], label='y')
    plt.plot(time_vec, yarr[:, 1], label="y'")
    plt.legend(loc='best')
    plt.show()


**Total running time of the script:** ( 0 minutes  0.015 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_odeint_damped_spring_mass.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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