aerosandbox.dynamics.utilities.lti_systems
==========================================

.. py:module:: aerosandbox.dynamics.utilities.lti_systems


Functions
---------

.. autoapisummary::

   aerosandbox.dynamics.utilities.lti_systems.peak_of_harmonic_oscillation


Module Contents
---------------

.. py:function:: peak_of_harmonic_oscillation(amplitude = 1, frequency_hz = 1, derivative_order = 0)

   Computes the peak value of the nth derivative of a simple harmonic oscillation (e.g., sine wave).

   Specifically, if `t` represents time, and we have an oscillation that is described by a function f(t) as:

       `f(t) = amplitude * sin(2 * pi * t * frequency_hz)`

   then this function will return the value of the nth time derivative of f(t), where `derivative_order` gives the
   value of n.

   .. rubric:: Example

   My spring-mass system has an oscillating position, where the mass oscillates in position from -0.1 to 0.1,
   with a frequency of 3 Hz. I want to know what the peak acceleration on that mass is:

   >>> peak_of_harmonic_oscillation(
   >>>     amplitude=0.1,
   >>>     frequency_hz=3,
   >>>     derivative_order=2
   >>> )

   This would return (2 * pi * 3) ^ 2 * 0.1, or around 35.5.

   So, the peak acceleration on my mass is around 35.5 m/s^2.

   :param amplitude: Amplitude of the underlying oscillation. Amplitude here is the center-to-peak distance,
   :param not peak-to-peak.:
   :param frequency_hz: Frequency of the underlying oscillation, in units of 1/time (Hz). Note: not the angular frequency.
   :param derivative_order: The derivative order. (E.g., 0 for position, 1 for velocity, 2 for acceleration).

   Returns: The peak value of the nth derivative of a simple harmonic oscillator with the specified amplitude and frequency.