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The Rhythm of Running: An Analysis of Preferred Running Tempo

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The action of running is difficult to measure, but well worth it to receive valuable information about one of our most basic evolutionary functions. In the context of modern day, recreational runners typically listen to music while running, and so

The action of running is difficult to measure, but well worth it to receive valuable information about one of our most basic evolutionary functions. In the context of modern day, recreational runners typically listen to music while running, and so the purpose of this experiment is to analyze the influence of music on running from a more dynamical approach. The first experiment was a running task involving running without a metronome and running with one while setting one's own preferred running tempo. The second experiment sought to manipulate the participant's preferred running tempo by having them listen to the metronome set at their preferred tempo, 20% above their preferred tempo, or 20% below. The purpose of this study is to analyze whether or not rhythmic perturbations different to one's preferred running tempo would interfere with one's preferred running tempo and cause a change in the variability of one's running patterns as well as a change in one's running performance along the measures of step rate, stride length, and stride pace. The evidence suggests that participants naturally entrained to the metronome tempo which influenced them to run faster or slower as a function of metronome tempo. However, this change was also accompanied by a shift in the variability of one's step rate and stride length.

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2017-05

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Modeling relationships between cycles in psychology: potential limitations of sinusoidal and mass-spring models

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With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series

With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series approaches that remove trends, cycles, and serial dependency have been used. These analyses permit the study of the relationship between random shocks (perturbations) in the presumed causal series and changes in the outcome series, but do not permit the study of the relationships between cycles. Liu and West (2016) proposed a multilevel approach that permitted the study of potential between subject relationships between features of the cycles in two series (e.g., amplitude). However, I show that the application of the Liu and West approach is restricted to a small set of features and types of relationships between the series. Several authors (e.g., Boker & Graham, 1998) proposed a connected mass-spring model that appears to permit modeling of more general cyclic relationships. I showed that the undamped connected mass-spring model is also limited and may be unidentified. To test the severity of the restrictions of the motion trajectories producible by the undamped connected mass-spring model I mathematically derived their connection to the force equations of the undamped connected mass-spring system. The mathematical solution describes the domain of the trajectory pairs that are producible by the undamped connected mass-spring model. The set of producible trajectory pairs is highly restricted, and this restriction sets major limitations on the application of the connected mass-spring model to psychological data. I used a simulation to demonstrate that even if a pair of psychological time-varying variables behaved exactly like two masses in an undamped connected mass-spring system, the connected mass-spring model would not yield adequate parameter estimates. My simulation probed the performance of the connected mass-spring model as a function of several aspects of data quality including number of subjects, series length, sampling rate relative to the cycle, and measurement error in the data. The findings can be extended to damped and nonlinear connected mass-spring systems.

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2019