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Concept: Simple harmonic motion


This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks-ad hoc designed and fabricated-which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit ‘sympathetic’ motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

Concepts: Scientific method, Science, Theory, Harmonic oscillator, Simple harmonic motion, Pendulum clock, Christiaan Huygens, Escapement


Acquired nystagmus, a highly symptomatic consequence of damage to the substrates of oculomotor control, often is resistant to pharmacotherapy. Although heterogeneous in its neural cause, its expression is unified at the effector-the eye muscles themselves-where physical damping of the oscillation offers an alternative approach. Because direct surgical fixation would immobilize the globe, action at a distance is required to damp the oscillation at the point of fixation, allowing unhindered gaze shifts at other times. Implementing this idea magnetically, herein we describe the successful implantation of a novel magnetic oculomotor prosthesis in a patient.

Concepts: Eye, Amputation, Harmonic oscillator, Pupil, Simple harmonic motion


Tapping or clapping to an auditory beat, an easy task for most individuals, reveals precise temporal synchronization with auditory patterns such as music, even in the presence of temporal fluctuations. Most models of beat-tracking rely on the theoretical concept of pulse: a perceived regular beat generated by an internal oscillation that forms the foundation of entrainment abilities. Although tapping to the beat is a natural sensorimotor activity for most individuals, not everyone can track an auditory beat. Recently, the case of Mathieu was documented (Phillips-Silver et al. 2011 Neuropsychologia 49, 961-969. (doi:10.1016/j.neuropsychologia.2011.02.002)). Mathieu presented himself as having difficulty following a beat and exhibited synchronization failures. We examined beat-tracking in normal control participants, Mathieu, and a second beat-deaf individual, who tapped with an auditory metronome in which unpredictable perturbations were introduced to disrupt entrainment. Both beat-deaf cases exhibited failures in error correction in response to the perturbation task while exhibiting normal spontaneous motor tempi (in the absence of an auditory stimulus), supporting a deficit specific to perception-action coupling. A damped harmonic oscillator model was applied to the temporal adaptation responses; the model’s parameters of relaxation time and endogenous frequency accounted for differences between the beat-deaf cases as well as the control group individuals.

Concepts: Quantum mechanics, Oscillation, Resonance, Normal mode, Harmonic oscillator, Simple harmonic motion, Pendulum, Ordinary differential equations


There is evidence that vibrations of soft tissue compartments are not appropriately described by a single sinusoidal oscillation for certain types of locomotion such as running or sprinting. This paper discusses a new method to quantify damping of superimposed oscillations using a wavelet-based time-frequency approach. This wavelet-based method was applied to experimental data in order to analyze the decay of the overall power of vibration signals over time. Eight healthy subjects performed sprinting trials on a 30m runway on a hard surface and a soft surface. Soft tissue vibrations were quantified from the tissue overlaying the muscle belly of the medial gastrocnemius muscle. The new methodology determines damping coefficients with an average error of 2.2% based on a wavelet scaling factor of 0.7. This was sufficient to detect differences in soft tissue compartment damping between the hard and soft surface. On average, the hard surface elicited a 7.02s(-1) lower damping coefficient than the soft surface (p<0.05). A power spectral analysis of the muscular vibrations occurring during sprinting confirmed that vibrations during dynamic movements cannot be represented by a single sinusoidal function. Compared to the traditional sinusoidal approach, this newly developed method can quantify vibration damping for systems with multiple vibration modes that interfere with one another. This new time-frequency analysis may be more appropriate when an acceleration trace does not follow a sinusoidal function, as is the case with multiple forms of human locomotion.

Concepts: Muscle, Tissues, Wave, Vibration, Harmonic oscillator, Simple harmonic motion, Damping, Mechanical vibrations


In the paper, we suggest a damped sinusoidal function be used to model a regenerative response of mucosa in time after the radiotherapy treatment. The medical history of 389 RT patients irradiated within the years 1994-2000 at the Radiotherapy Department, Cancer Center, Maria Skłodowska-Curie Memorial Institute of Oncology, Gliwice, Poland, was taken into account. In the analyzed group of patients, the number of observations of a single patient ranged from 2 to 25 (mean = 8.3, median = 8) with severity determined by use of Dische’s scores from 0 to 24 (mean = 7.4, median = 7). Statistical modeling of radiation-induced mucositis was performed for five groups of patients irradiated within the following radiotherapy schedules: CAIR, CB, Manchester, CHA-CHA, and Conventional. All of the regression parameters of the assumed model, i.e. amplitude, damping coefficient, angular frequency, phase of component, and offset, estimated in the analysis were statistically significant (p-value < 0.05) for the radiotherapy schedules. The model was validated using a non-oscillatory function. Following goodness-of-fit statistics, the damped sinusoidal function fits the data better than the non-oscillatory damped function. Model curves for harmonic characteristics with confidence intervals were plotted separately for each of the RT schedules and together in a combined design. The suggested model might be helpful in the numeric evaluation of the RT toxicity in the groups of patients under analysis as it allows for practical comparisons and treatment optimization. A statistical approach is also briefly described in the paper.

Concepts: Statistics, Mathematics, Chemotherapy, Wave, Phase, Confidence interval, Statistical hypothesis testing, Simple harmonic motion


In diagnostic medicine, microbubbles are used as contrast agents to image blood flow and perfusion in large and small vessels. The small vessels (the capillaries) have diameters from a few hundred micrometers down to less than 10 μ m. The effect of such microvessels surrounding the oscillating microbubbles is currently unknown, and is important for increased sensitivity in contrast diagnostics and manipulation of microbubbles for localized drug release. Here, oscillations of microbubbles in tubes with inner diameters of 25 μm and 160 ¿m are investigated using an ultra-high-speed camera at frame rates of ~12 million frames/s. A reduction of up to 50% in the amplitude of oscillation was observed for microbubbles in the smaller 25-μm tube, compared with those in a 160-μm tube. In the 25-μm tube, at 50 kPa, a 48% increase of microbubbles that did not oscillate above the noise level of the system was observed, indicating increased oscillation damping. No difference was observed between the resonance frequency curves calculated for microbubbles in 25-μm and 160-μm tubes. Although previous investigators have shown the effect of microvessels on microbubble oscillation at high ultrasound pressures, the present study provides the first optical images of low-amplitude microbubble oscillations in small tubes.

Concepts: Resonator, Oscillation, Wave, Feedback, Beat, Harmonic oscillator, Simple harmonic motion


To see that positive and negative effects of training induce apparent oscillations of performance, suggesting that the delayed cumulative effects of training on daily performance capacity (DPC) are best fitted by sine waves damped over time. The aim of this study is to compare the criterion validity of Impulse Response (IR) model of Banister and damped harmonic oscillation model (DHO) for quantifying training load (TL)-DPC relationship.

Concepts: Oscillation, Wave, Validity, Criterion validity, Periodic function, Harmonic oscillator, Sine wave, Simple harmonic motion


How signaling dynamics encode information is a central question in biology. During vertebrate development, dynamic Notch signaling oscillations control segmentation of the presomitic mesoderm (PSM). In mouse embryos, this molecular clock comprises signaling oscillations of several pathways, i.e., Notch, Wnt, and FGF signaling. Here, we directly address the role of the relative timing between Wnt and Notch signaling oscillations during PSM patterning. To this end, we developed a new experimental strategy using microfluidics-based entrainment that enables specific control of the rhythm of segmentation clock oscillations. Using this approach, we find that Wnt and Notch signaling are coupled at the level of their oscillation dynamics. Furthermore, we provide functional evidence that the oscillation phase shift between Wnt and Notch signaling is critical for PSM segmentation. Our work hence reveals that dynamic signaling, i.e., the relative timing between oscillatory signals, encodes essential information during multicellular development.

Concepts: Developmental biology, Developed country, Oscillation, Wave, Phase, Modulation, Feedback, Simple harmonic motion


Systems of coupled oscillators abound in nature. How they establish stable phase relationships under diverse conditions is fundamentally important. The mammalian suprachiasmatic nucleus (SCN) is a self-sustained, synchronized network of circadian oscillators that coordinates daily rhythms in physiology and behavior. To elucidate the underlying topology and signaling mechanisms that modulate circadian synchrony, we discriminated the firing of hundreds of SCN neurons continuously over days. Using an analysis method to identify functional interactions between neurons based on changes in their firing, we characterized a GABAergic network comprised of fast, excitatory, and inhibitory connections that is both stable over days and changes in strength with time of day. By monitoring PERIOD2 protein expression, we provide the first evidence that these millisecond-level interactions actively oppose circadian synchrony and inject jitter into daily rhythms. These results provide a mechanism by which circadian oscillators can tune their phase relationships under different environmental conditions.

Concepts: Nervous system, DNA, Hypothalamus, Action potential, Oscillation, Wave, Feedback, Simple harmonic motion


Models for bacterial adhesion to substratum surfaces all include uncertainty with respect to the (ir)reversibility of adhesion. In a model, based on vibrations exhibited by adhering bacteria parallel to a surface, adhesion was described as a result of reversible binding of multiple bacterial tethers that detach from and successively re-attach to a surface, eventually making bacterial adhesion irreversible. Here, we use Total Internal Reflection Microscopy to determine whether adhering bacteria also exhibit variations over time in their perpendicular distance above surfaces. Streptococci with fibrillar surface tethers showed perpendicular vibrations with amplitudes of around 5 nm, regardless of surface hydrophobicity. Adhering, non-fibrillated streptococci vibrated with amplitudes around 20 nm above a hydrophobic surface. Amplitudes did not depend on ionic strength for either strain. Calculations of bacterial energies from their distances above the surfaces using the Boltzman equation showed that bacteria with fibrillar tethers vibrated as an harmonic oscillator. The energy of bacteria without fibrillar tethers varied with distance in a comparable fashion as the DLVO (Derjaguin, Landau, Verwey and Overbeek)-interaction energy. Distance variations above the surface over time of bacteria with fibrillar tethers are suggested to be governed by the harmonic oscillations, allowed by elasticity of the tethers, piercing through the potential energy barrier. Bacteria without fibrillar tethers “float” above a surface in the secondary energy minimum, with their perpendicular displacement restricted by their thermal energy and the width of the secondary minimum. The distinction between “tether-coupled” and “floating” adhesion is new, and may have implications for bacterial detachment strategies.  .

Concepts: Energy, Hydrophobe, Kinetic energy, Oscillation, Potential energy, Analytic geometry, Harmonic oscillator, Simple harmonic motion