aerosandbox.dynamics.utilities.lti_systems#

Module Contents#

Functions#

peak_of_harmonic_oscillation([amplitude, ...])

Computes the peak value of the nth derivative of a simple harmonic oscillation (e.g., sine wave).
aerosandbox.dynamics.utilities.lti_systems.peak_of_harmonic_oscillation(amplitude=1, frequency_hz=1, derivative_order=0)[source]#

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.

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.

Parameters:

  • amplitude (float) – Amplitude of the underlying oscillation. Amplitude here is the center-to-peak distance,

  • peak-to-peak. (not) –

  • frequency_hz (float) – Frequency of the underlying oscillation, in units of 1/time (Hz). Note: not the angular frequency.

  • derivative_order (int) – 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.