A Solution to the Response of a Single Degree of Freedom System to Swept Sine Inputs
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Bibliographic record
Abstract
This paper presents a solution of the response of a single-degree-of-freedom system to swept sine input. Including the derivations for how this solution was obtained. This solution includes the time-domain response to a linearly varying swept sine input. The time-domain response includes the transient response of the system. The solution is simplified, so it can easily be computed by software packages. The Pearson correlation coefficient is measured between the solution presented in this paper and the Runge-Kutta simulation to measure the accuracy of the solution presented. Comparison of the time-domain response to similar results obtained from Runge-Kutta simulation of various systems shows excellent agreement. Results from a physical beam are also compared and shows good agreement. From the time-domain response, the frequency response functions are generated by taking the Fourier transform of the response. The frequency response functions of the response also show excellent agreement with those obtained via theoretical singledegree frequency results. The agreement of the time domain results is maintained even when non-ideal swept sine parameters are chosen. This paper also presents a method for ensuring the transient responses of the system have died out for when swept sines are used to measure the frequency response of a system.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it