.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_09_resonance.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_09_resonance.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_09_resonance.py:


Resonance curve
===============

The amplitude of a driven oscillator near resonance is approximately Lorentzian. The quality
factor follows from the resonance frequency and the width: Q = f₀ / (2γ), where γ is the half
width at half maximum. The detector has a small constant offset.

.. GENERATED FROM PYTHON SOURCE LINES 11-22

.. code-block:: Python

    import numpy as np

    import fitwise as fw

    rng = np.random.default_rng(9)
    f = np.linspace(950, 1050, 101)  # Hz
    amplitude = 2.4 * 4.0**2 / ((f - 1002.5) ** 2 + 4.0**2) + 0.05 + rng.normal(0, 0.02, f.size)

    result = fw.fit(fw.models.lorentzian + fw.models.constant, f, amplitude, yerr=0.02)
    print(result)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Model:      lorentzian(x; amp, cen, gamma) + constant(x; c)
    Method:     Trust Region Reflective (scipy least_squares) (auto: nonlinear)
    Converged:  yes (24 evals)
    Data:       101 points, yerr given (absolute)
    Start:      amp, cen, gamma: peak heuristic · c: edge baseline

    Parameter      Value   ± Std.Err    Rel.   Bounds
    amp            2.392       0.011   0.5 %   –
    cen         1002.499       0.019   0.0 %   –
    gamma          3.984       0.030   0.8 %   –
    c             0.0521      0.0026   4.9 %   –

    χ²/ndf = 1.03 (97 dof, p = 0.41)    R² = 0.9986    AIC = 6.4
    Correlations > 0.5:  amp–gamma (-0.60)
    Warnings:   none




.. GENERATED FROM PYTHON SOURCE LINES 23-29

.. code-block:: Python

    f0, gamma = result.params["cen"], result.params["gamma"]
    Q = f0.value / (2 * gamma.value)
    print(
        f"f0 = {f0.value:.2f} ± {f0.stderr:.2f} Hz,  Q = {Q:.0f} ± {Q * gamma.stderr / gamma.value:.0f}"
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    f0 = 1002.50 ± 0.02 Hz,  Q = 126 ± 1




.. GENERATED FROM PYTHON SOURCE LINES 30-33

.. code-block:: Python

    fig, axes = result.plot()
    axes[0].set_ylabel("amplitude (V)")
    axes[1].set_xlabel("f (Hz)")



.. image-sg:: /auto_examples/images/sphx_glr_plot_09_resonance_001.png
   :alt: plot 09 resonance
   :srcset: /auto_examples/images/sphx_glr_plot_09_resonance_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 18.503588541666666, 'f (Hz)')




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

   **Total running time of the script:** (0 minutes 0.120 seconds)


.. _sphx_glr_download_auto_examples_plot_09_resonance.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_09_resonance.ipynb <plot_09_resonance.ipynb>`

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

      :download:`Download Python source code: plot_09_resonance.py <plot_09_resonance.py>`

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

      :download:`Download zipped: plot_09_resonance.zip <plot_09_resonance.zip>`


.. only:: html

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

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