aerosandbox.dynamics.utilities.lti_systems
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Module Contents#
Functions#
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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.