LYCOS RETRIEVER 
Harmonic Oscillator
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Harmonic oscillators occurring in a number of areas of engineering are equivalent in the sense that their mathematical models are identical (see universal oscillator equation above). Below is a table showing analogous quantities in four harmonic oscillator systems in mechanics and electronics. If analogous parameters on the same line in the table are given numerically equal values, the behavior of the oscillators will be the same.
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A harmonic oscillator with distinct resonances can be shown with gliders and springs on an air track. For example, for a string of gliders there are as many resonances as there are gliders on the track. As one adds gliders great stability requirements are placed on the sine drive which is used to drive the gliders. The Precision Sine Drive uses a stepping motor which is locked to the drive oscillator. The frequency of the motor drive can be determined with a frequency meter. Resonance frequencies can be easily reset by adjusting the drive to the monitored output shown on the frequency meter.
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The goal of this document is to have students explore the solutions to the quantum mechanical harmonic oscillator Schrodinger equation. . Students examine the exponential component, generate and examine various Hermite polynomials, and create the final HO wavefunctions as a product of a normalization factor, the exponential component, and a Hermite polynomial. Students ... are prepare graphs of several Harmonic oscillator solutions and the probability density functions. Using Mathcad is an effective way for them to draw their own figures and master understanding of the concepts involved.
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The goal of this document is to have students explore the solutions to the quantum mechanical harmonic oscillator Schrödinger equation. Students do this by examining the exponential component, generating the various Hermite polynomials, and then creating the final HO wave functions as a product of a normalization factor, the exponential component, and a Hermite polynomial. Students ... prepare plots of several harmonic oscillator wave functions and probability densities. The plots created with Mathcad provide an effective way for students to draw their own figures and master understanding of the concepts involved. Finally, students can examine the plots at both high and low quantum numbers and correlate their observations with classical harmonic oscillator predictions of maximum and minimum kinetic energy and maximum probability of the extension of the oscillator.
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The harmonic oscillator consists of a mass m, attracted to a certain origin by a force F. The force is proportional to the distance x of the mass with respect to the origin. The coefficient that relates the distance from the origin to the attracting force is called a.
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A model for harmonic oscillator damping due to the internal friction of solids has been developed, based on considerations of a long period pendulum. The assumption of a complex elastic modulus to describe stress-strain hysteresis in the support structure of the pendulum yields an expression for the figure of merit Q that agrees with many experiments involving material damping. As such, the approximations of this linear model stand in contrast with common theory.
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Harmonic Oscillator