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Simple Harmonic Motion

Simple Harmonic Motion

Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke's law. If the net force can be described by Hooke's law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position. To derive an equation for period and frequency, the equation of motion is used. The period of a simple harmonic oscillator is given...

Modes of Standing Waves - I

Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...

Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Characteristics of Simple Harmonic Motion

Characteristics of Simple Harmonic Motion

The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...

Simple Harmonic Motion and Uniform Circular Motion

Simple Harmonic Motion and Uniform Circular Motion

While simple harmonic motion and uniform circular motion may be two separate concepts, they correlate and interlink with each other. Simple harmonic motion is an oscillatory motion in a system where the net force can be described by Hooke's law, while uniform circular motion is the motion of an object in a circular path at constant speed.
There is an easy way to produce simple harmonic motion by using uniform circular motion. For instance, consider a ball attached to a uniformly rotating...

Energy in Simple Harmonic Motion

Energy in Simple Harmonic Motion

To determine the energy of a simple harmonic oscillator, consider all the forms of energy it can have during its simple harmonic motion. According to Hooke's Law, the energy stored during the compression/stretching of a string in a simple harmonic oscillator is potential energy. As the simple harmonic oscillator has no dissipative forces, it also possesses kinetic energy. In the presence of conservative forces, both energies can interconvert during oscillation, but the total energy remains...

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Data Processing Methods for 3D Seismic Imaging of Subsurface Volcanoes: Applications to the Tarim Flood Basalt

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Mathematical model for volcanic harmonic tremors.

Giordano Montegrossi^1,2, Angiolo Farina³, Lorenzo Fusi^4,3

¹IGG Istituto Geoscienze e Georisorse, CNR, Via la Pira 4, Firenze, 50121, Italy. montegrossi@igg.cnr.it.

Scientific Reports

|October 10, 2019

Summary

Volcanic harmonic tremors are caused by oscillating bubbles in cavities. A new mathematical model accurately predicts tremor frequency based on physical parameters, validated by experiments and literature.

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Area of Science:

Geophysics
Volcanology
Acoustics

Background:

Harmonic tremors release infrasonic energy during volcanic activity.
These tremors typically occur within the 0.1-12 Hz frequency range.
A prevailing hypothesis links tremors to oscillating bubbles in volcanic cavities converting thermal to mechanical energy.

Purpose of the Study:

To develop a mathematical model for volcanic harmonic tremors.
To describe the oscillatory mechanism of bubble formation in cavities.
To determine tremor frequency as a function of key physical parameters.

Main Methods:

An experimental apparatus was designed to replicate the natural phenomenon.
A mathematical model was formulated to simulate the oscillatory mechanism.
Model-derived frequencies were compared with experimental and literature data.

Main Results:

The mathematical model successfully describes the oscillatory mechanism of bubble formation.
The model predicts tremor frequencies that align with experimental measurements.
Model predictions are consistent with existing data from scientific literature.

Conclusions:

The proposed mathematical model accurately represents volcanic harmonic tremors.
The model provides a reliable method for predicting tremor frequency.
This research validates the bubble oscillation hypothesis for harmonic tremor generation.