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Articles 27451 - 27480 of 36719

Full-Text Articles in Physical Sciences and Mathematics

Wide Angle Decentered Lens Beam Steering For Infrared Countermeasures Applications, Jennifer L. Gibson, Bradley D. Duncan, Edward A. Watson, John S. Loomis Oct 2004

Wide Angle Decentered Lens Beam Steering For Infrared Countermeasures Applications, Jennifer L. Gibson, Bradley D. Duncan, Edward A. Watson, John S. Loomis

Electro-Optics and Photonics Faculty Publications

A beam-steering system consisting of three cemented achromatic doublets is presented. Intended for use in IR countermeasure applications, our system is designed to operate over the 2- to 5-μm spectrum with minimum angular dispersion. We show that dispersion can be minimized by using doublet lenses fashioned from AMTIR-1 and germanium. Our system is designed to be compact and lightweight, with no internal foci, while allowing steering to ±22.5 deg. We also maintain a minimum 2-in. clear aperture for all steering angles, and a nominal divergence of 1 mrad. Plane wave and Gaussian beam analyses of our system are presented.


Response Of The Martian Thermosphere/Ionosphere To Enhanced Fluxes Of Solar Soft X Rays, Jane L. Fox Oct 2004

Response Of The Martian Thermosphere/Ionosphere To Enhanced Fluxes Of Solar Soft X Rays, Jane L. Fox

Physics Faculty Publications

We have investigated the response of the thermosphere and ionosphere of Mars to enhanced fluxes of solar soft X rays, such as those that have been detected by the SNOE satellite (e.g., Bailey et al., 2000 ). We have constructed standard models by adopting the SC#21REFW and F79050N solar fluxes from H. E. Hinteregger (private communication) (see also Torr et al., 1979 ) for the low and high solar activity models, respectively. We then constructed enhanced soft X-ray models by multiplying the solar photon fluxes for wavelengths below 200 Å by a factor of 3 at low solar …


Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin Oct 2004

Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin

Physics Faculty Research & Creative Works

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order α ( Z α )4 to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order α2 ( Z α )4 ln [ ( Z α )- 2 ] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for …


Fully Differential Three-Dimensional Angular Distributions Of Electrons Ionized In Ion-Atom Collisions, Michael Schulz, R. Moshammer, Daniel Fischer, Ahmad Hasan, N. V. Maydanyuk, J. D. Ullrich Oct 2004

Fully Differential Three-Dimensional Angular Distributions Of Electrons Ionized In Ion-Atom Collisions, Michael Schulz, R. Moshammer, Daniel Fischer, Ahmad Hasan, N. V. Maydanyuk, J. D. Ullrich

Physics Faculty Research & Creative Works

We compare experimental fully differential three-dimensional angular distributions of electrons ionized from He in collision with ionic projectiles covering a broad range of perturbations (0.065 to 4.4). Even at very small perturbations clear signatures of higher-order contributions are observable. At large perturbations, such contributions become even dominant, especially those involving the post-collision interaction between the outgoing projectile and the ionized electron. Our results show that single ionization is not nearly as well understood as was assumed previously.


Nucleation Near The Spinodal: Limitations Of Mean Field Density Functional Theory, Gerald Wilemski, Jin-Song Li Oct 2004

Nucleation Near The Spinodal: Limitations Of Mean Field Density Functional Theory, Gerald Wilemski, Jin-Song Li

Physics Faculty Research & Creative Works

We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory ~GT! of van der Waals and Cahn and Hilliard and mean field density functional theory ~MFDFT!. As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Dg satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the …


Cross Sections Fall 2004, Department Of Physics And Astronomy Oct 2004

Cross Sections Fall 2004, Department Of Physics And Astronomy

Cross Sections

No abstract provided.


On The Polarization Of Closed Strings By Ramond-Ramond Fluxes, Vatche Sahakian Oct 2004

On The Polarization Of Closed Strings By Ramond-Ramond Fluxes, Vatche Sahakian

All HMC Faculty Publications and Research

In the Green-Schwarz formalism, the closed string worldsheet of the IIB theory couples to Ramond-Ramond (RR) fluxes through spinor bilinears. We study the effect of such fluxes by analyzing the supersymmetry transformation of the worldsheet in general backgrounds. We show that, in the presence RR fields, the closed string can get `polarized', as the spinors acquire non-zero vevs in directions correlating with the orientation of close-by D-branes. Reversing the argument, this may allow for worldsheet configurations—with non-trivial spinor structure—that source RR moments.


Measurement Of The Tt̅ Production Cross Section In Pp̅ Collisions At √S =1.96 Tev Using Dilepton Events, Darin Acosta, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration Oct 2004

Measurement Of The Tt̅ Production Cross Section In Pp̅ Collisions At √S =1.96 Tev Using Dilepton Events, Darin Acosta, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration

Kenneth Bloom Publications

We report a measurement of the tt̅ production cross section using dilepton events with jets and missing transverse energy in pp̅ collisions at a center-of-mass energy of 1.96 TeV. Using a 197±12 pb-1 data sample recorded by the upgraded Collider Detector at Fermilab, we use two complementary techniques to select candidate events. We compare the number of observed events and selected kinematical distributions with the predictions of the standard model and find good agreement. The combined result of the two techniques yields a tt̅ production cross section of 7.0-2.1+2.4 (stat) -1.1+1.6 (syst)±0.4(lum) pb.


Inclusive Double-Pomeron Exchange At The Fermilab Tevatron P̅P Collider, Darin Acosta, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration Oct 2004

Inclusive Double-Pomeron Exchange At The Fermilab Tevatron P̅P Collider, Darin Acosta, Kenneth A. Bloom, Collider Detector At Fermilab Collaboration

Kenneth Bloom Publications

We report results from a study of events with a double-Pomeron exchange topology produced in p̅p collisions at √s =1800 GeV. The events are characterized by a leading antiproton and a large rapidity gap on the outgoing proton side. We find that the differential production cross section agrees in shape with predictions based on Regge theory and factorization, and that the ratio of double-Pomeron exchange to single diffractive production rates is relatively unsuppressed as compared to the θ(10) suppression factor previously measured in single diffractive production.


Spatiotemporal Distribution Of Marine Magnetotactic Bacteria In A Seasonally Stratified Coastal Salt Pond, S. L. Simmons, S. M. Sievert, Richard B. Frankel, Dennis A. Bazylinski, K. J. Edwards Oct 2004

Spatiotemporal Distribution Of Marine Magnetotactic Bacteria In A Seasonally Stratified Coastal Salt Pond, S. L. Simmons, S. M. Sievert, Richard B. Frankel, Dennis A. Bazylinski, K. J. Edwards

Physics

The occurrence and distribution of magnetotactic bacteria (MB) were studied as a function of the physical and chemical conditions in meromictic Salt Pond, Falmouth, Mass., throughout summer 2002. Three dominant MB morphotypes were observed to occur within the chemocline. Small microaerophilic magnetite-producing cocci were present at the top of the chemocline, while a greigite-producing packet-forming bacterium occurred at the base of the chemocline. The distributions of these groups displayed sharp changes in abundance over small length scales within the water column as well as strong seasonal fluctuations in population abundance. We identified a novel, greigite-producing rod in the sulfidic hypolimnion …


Event Rate Estimates For Lisa Extreme Mass Ratio Capture Sources, J. Gair, L. Barack, T. Creighton, C. Cutler, Shane L. Larson, E. S. Phinney, M. Vallisneri Oct 2004

Event Rate Estimates For Lisa Extreme Mass Ratio Capture Sources, J. Gair, L. Barack, T. Creighton, C. Cutler, Shane L. Larson, E. S. Phinney, M. Vallisneri

All Physics Faculty Publications

One of the most exciting prospects for the LISA gravitational wave observatory is the detection of gravitational radiation from the inspiral of a compact object into a supermassive black hole. The large inspiral parameter space and low amplitude of the signal make detection of these sources computationally challenging. We outline here a first-cut data analysis scheme that assumes realistic computational resources. In the context of this scheme, we estimate the signal-to-noise ratio that a source requires to pass our thresholds and be detected. Combining this with an estimate of the population of sources in the universe, we estimate the number …


Photometry Of Type Ii Cepheids. I. The Long-Period Stars, Edward G. Schmidt, Dale Johnston, Shawn Langan, Kevin M. Lee Oct 2004

Photometry Of Type Ii Cepheids. I. The Long-Period Stars, Edward G. Schmidt, Dale Johnston, Shawn Langan, Kevin M. Lee

Department of Physics and Astronomy: Faculty Publications

We present 1256 new photometric observations of 36 Cepheids with periods longer than 8 days. The majority are likely type II Cepheids, but we have included about a dozen classical Cepheids for comparison purposes, a few stars of uncertain type, and one putative RV Tauri star. We discuss the appearance of the light curves, the Fourier parameters, and the light-curve stability in terms of differentiation between type I and type II Cepheids. Although we encounter the same difficulties as previous investigators in using these parameters for this purpose, we are able to identify some stars of particular interest, including several …


Lorentz-Violating Electrostatics And Magnetostatics, Quentin G. Bailey, V. Alan Kostelecký Oct 2004

Lorentz-Violating Electrostatics And Magnetostatics, Quentin G. Bailey, V. Alan Kostelecký

Publications

Electromagnetostatics experiments show promise for improving existing sensitivities to parity-odd coefficients for Lorentz violation in the photon sector.


Asymptotic Accuracy Of Geoacoustic Inversions, Michele Zanolin, Ian Ingram, Aaron Thode, Nicholas C. Makris Oct 2004

Asymptotic Accuracy Of Geoacoustic Inversions, Michele Zanolin, Ian Ingram, Aaron Thode, Nicholas C. Makris

Publications

Criteria necessary to accurately estimate a set of unknown geoacoustic parameters from remote acoustic measurements are developed in order to aid the design of geoacoustic experiments. The approach is to have estimation error fall within a specified design threshold by adjusting controllable quantities such as experimental sample size or signal-to-noise ratio (SNR). This is done by computing conditions on sample size and SNR necessary for any estimate to have a variance that (1) asymptotically attains the Cramer–Rao lower bound (CRLB) and (2) has a CRLB that falls within the specified design error threshold. Applications to narrow band deterministic signals received …


Analysis Of Chaos-Induced Pulse Trains In The Ionization Of Hydrogen, K. A. Mitchell, J. P. Handley, B. Tighe, A. Flower, John B. Delos Oct 2004

Analysis Of Chaos-Induced Pulse Trains In The Ionization Of Hydrogen, K. A. Mitchell, J. P. Handley, B. Tighe, A. Flower, John B. Delos

Arts & Sciences Articles

We examine excitation (by a short laser pulse) of a hydrogen atom in parallel electric and magnetic fields, from an initial tightly bound state to a state above the classical ionization threshold. We predict that the atom ionizes by emitting a train of electron pulses. This prediction is based on the classical dynamics of electron escape. In particular, the pulse train is due to classical chaos, which occurs for nonvanishing magnetic field. We connect the structure of the pulse train to fractal structure in the escape dynamics, and discuss several issues of experimental interest, with a particular emphasis on understanding …


Vector Operations In Superscalar Architectures, Nathan Daniel Flinn Oct 2004

Vector Operations In Superscalar Architectures, Nathan Daniel Flinn

Electrical & Computer Engineering Theses & Dissertations

Vector calculations are very prevalent today. Though the vector-processing computer is quite an old concept, superscalar processors lack hardware support for vector operations. This thesis investigates whether an ordinary superscalar computer architecture can be designed to include hardware support for improved vector operations without drastically changing the existing superscalar design and behavior. A computer architecture design was created and implemented that included the vector multiply (dot product) operation. The design includes a Vector Operations Unit that captures incoming vector operations and generates the necessary set of machine instructions to complete the vector operation internally. It then delivers these instructions to …


Modeling And Simulation Of Photonic Crystal Fibers Using Finite Difference Frequency Domain Method, Md. Khalid Ikram Oct 2004

Modeling And Simulation Of Photonic Crystal Fibers Using Finite Difference Frequency Domain Method, Md. Khalid Ikram

Electrical & Computer Engineering Theses & Dissertations

Photonic crystal fibers (PCFs) allow guiding light in low-index core. These fibers exhibit properties such as single-mode operation in broad wavelength region. The mode shape and group velocity dispersion can be controlled by designing the microstructures of the cladding. In order to study these properties, a fast, efficient, and highly accurate numerical modeling method is required.

A full-vectorial finite-difference frequency-domain (FDFD) method is implemented. The modal properties of conventional step index fiber and index-guiding PCF are analyzed using this modeling technique. Compared to plane wave expansion and biorthogonal basis methods, FDFD is found to be simple, reliable, and efficient. PCFs …


Simulation Of High Intensity Laser Pulse Propagation Through Optical Systems, Jeremy Gulley, Erik Zeek, William Dennis Sep 2004

Simulation Of High Intensity Laser Pulse Propagation Through Optical Systems, Jeremy Gulley, Erik Zeek, William Dennis

Jeremy R. Gulley

No abstract is currently available.


Asymptotic Accuracy Of Geoacoustic Inversions, Michele Zanolin, Ian Ingram, Aaron Thode, Nicholas C. Makris Sep 2004

Asymptotic Accuracy Of Geoacoustic Inversions, Michele Zanolin, Ian Ingram, Aaron Thode, Nicholas C. Makris

Michele Zanolin

Criteria necessary to accurately estimate a set of unknown geoacoustic parameters from remote acoustic measurements are developed in order to aid the design of geoacoustic experiments. The approach is to have estimation error fall within a specified design threshold by adjusting controllable quantities such as experimental sample size or signal-to-noise ratio (SNR). This is done by computing conditions on sample size and SNR necessary for any estimate to have a variance that (1) asymptotically attains the Cramer–Rao lower bound (CRLB) and (2) has a CRLB that falls within the specified design error threshold. Applications to narrow band deterministic signals received …


Stimulated Raman Backscattering Of Laser Radiation In Deep Plasma Channels, Serguei Y. Kalmykov, Gennady Shvets Sep 2004

Stimulated Raman Backscattering Of Laser Radiation In Deep Plasma Channels, Serguei Y. Kalmykov, Gennady Shvets

Serge Youri Kalmykov

Stimulated Raman backscattering (RBS) of intense laser radiation confined by a single-mode plasma channel with a radial variation of plasma frequency greater than a homogeneous-plasma RBS bandwidth is characterized by a strong transverse localization of resonantly driven electron plasma waves (EPW). The EPW localization reduces the peak growth rate of RBS and increases the amplification bandwidth. The continuum of nonbound modes of backscattered radiation shrinks the transverse field profile in a channel and increases the RBS growth rate. Solution of the initial-value problem shows that an electromagnetic pulse amplified by the RBS in the single-mode deep plasma channel has a …


Thermoelectricity In Natural And Synthetic Hydrogels, Brandon R. Brown Sep 2004

Thermoelectricity In Natural And Synthetic Hydrogels, Brandon R. Brown

Physics and Astronomy

We describe a technique for measuring a Seebeck effect in gels and present data for three systems. notably distinct signals are obtained for gel originating in the electrosensitive organs of marine sharks, syntehtic collagen-based gel, and as a control, seawater, the gels' seawater simply confirms that gels suppress mass transport. The difference between synthetic gel and the gel of sharks shows that the charged polymers of the shark gel restrict mass transport much more successfully than the polumers of the collagen gel, and we submit that this sort of ion localization is key to the emergence of thermoelectricity in a …


Production Of E+E Pairs Accompanied By Nuclear Dissociation In Ultraperipheral Heavy-Ion Collisions, Star Collaboration, T.D. Gutierrez Sep 2004

Production Of E+E− Pairs Accompanied By Nuclear Dissociation In Ultraperipheral Heavy-Ion Collisions, Star Collaboration, T.D. Gutierrez

Physics

We present data on e+e pair production accompanied by nuclear breakup in ultraperipheral gold-gold collisions at a center of mass energy of 200GeV per nucleon pair. The nuclear breakup requirement selects events at small impact parameters, where higher-order diagrams for pair production should be enhanced. We compare the data with two calculations: one based on the equivalent photon approximation, and the other using lowest-order quantum electrodynamics (QED). The data distributions agree with both calculations, except that the pair transverse momentum spectrum disagrees with the equivalent photon approach. We set limits on higher-order contributions to the cross section.


Production Of A Kev X-Ray Beam From Synchrotron Radiation In Relativistic Laser-Plasma Interaction, Antoine Rousse, Kim Ta Phuoc, Rahul Shah, Alexander Pukhov, Eric Lefebvre, Victor Malka, Sergey Kiselev, Frederic Burgy, Jean-Philippe Rousseau, Donald P. Umstadter, Daniele Hulin Sep 2004

Production Of A Kev X-Ray Beam From Synchrotron Radiation In Relativistic Laser-Plasma Interaction, Antoine Rousse, Kim Ta Phuoc, Rahul Shah, Alexander Pukhov, Eric Lefebvre, Victor Malka, Sergey Kiselev, Frederic Burgy, Jean-Philippe Rousseau, Donald P. Umstadter, Daniele Hulin

Donald Umstadter Publications

We demonstrate that a beam of x-ray radiation can be generated by simply focusing a single high-intensity laser pulse into a gas jet. A millimeter-scale laser-produced plasma creates, accelerates, and wiggles an ultrashort and relativistic electron bunch. As they propagate in the ion channel produced in the wake of the laser pulse, the accelerated electrons undergo betatron oscillations, generating a femtosecond pulse of synchrotron radiation, which has keV energy and lies within a narrow (50 mrad) cone angle.


First Principles Study Of Transition-Metal Substitutions In Sm–Co Permanent Magnets, Renat F. Sabirianov, Arti Kashyap, Ralph Skomski, Sitaram Jaswal, David J. Sellmyer Sep 2004

First Principles Study Of Transition-Metal Substitutions In Sm–Co Permanent Magnets, Renat F. Sabirianov, Arti Kashyap, Ralph Skomski, Sitaram Jaswal, David J. Sellmyer

David Sellmyer Publications

The microchemistry and magnetism of conventional and high-temperature Sm–Co permanent magnets are investigated by first-principles calculations. Particular emphasis is on the site preference for the substitution of Cu, Ti, and Zr in SmCo5 and Sm2Co17 compounds. Cu substitution is more favorable in the 1:5 phase, in agreement with experimental findings. Titanium and zirconium have positive solution energies for both the phases, with Ti(Zr) having slight preference for the 1:5 (2:17) phase. Some Zr may segregate to the phase boundaries because of its large solution energy. For Ti and Zr the dumbbell site of the 2:17 phase …


Polarization-Dependent Electron Affinity Of Linbo3 Surfaces, W.-C. Yang, B. J. Rodriguez, Alexei Gruverman, R. J. Nemanich Sep 2004

Polarization-Dependent Electron Affinity Of Linbo3 Surfaces, W.-C. Yang, B. J. Rodriguez, Alexei Gruverman, R. J. Nemanich

Alexei Gruverman Publications

Polar surfaces of a ferroelectric LiNbO3 crystal with periodically poled domains are explored using UV-photoelectron emission microscopy (PEEM). Compared with the positive domains (domains with positive surface polarization charges), a higher photoelectric yield is found from the negative domains (domains with negative surface polarization charges), indicating a lower photothreshold and a corresponding lower electron affinity. The photon-energy-dependent contrast in the PEEM images of the surfaces indicates that the photothreshold of the negative domains is ~4.6 eV while that of the positive domains is greater than ~6.2 eV. We propose that the threshold difference between the opposite domains can be …


Stark Width And Shift Of The Neutral Argon 425.9 Nm Spectral Line, Vladimir Milosavljevic, Vida Zigman, Stevan Djenize Sep 2004

Stark Width And Shift Of The Neutral Argon 425.9 Nm Spectral Line, Vladimir Milosavljevic, Vida Zigman, Stevan Djenize

Articles

The Stark parameters, the width (W) and the shift (d), of the neutral argon (Ar I) 425.9 nm spectral line have been studied in a linear, low-pressure, optically thin pulsed arc discharge. The line shapes are measured in three different plasmas at about 16,000 K electron temperature (T) and about 7.0×1022 m−3 electron density (N). The separate electron and ion contributions to the total Stark width (Wt), i.e. We and Wi, as well as to the total Stark shift (dt), i.e. …


Superconducting Transition Edge Sensor Using Dilute Almn Alloys, S. W. Deiker, W. Doriese, G. C. Hilton, K. D. Hilton, W. H. Rippard, J. N. Ullom, L. R. Vale, S. T. Ruggiero, A. Williams, Betty A. Young Sep 2004

Superconducting Transition Edge Sensor Using Dilute Almn Alloys, S. W. Deiker, W. Doriese, G. C. Hilton, K. D. Hilton, W. H. Rippard, J. N. Ullom, L. R. Vale, S. T. Ruggiero, A. Williams, Betty A. Young

Physics

We have fabricated a bolometer using a transition-edge sensor (TES) made of Al doped with Mn to suppress the superconducting critical temperature (Tc) of Al from ∼1Kto∼100mK. The resulting detector exhibits low-frequency noise consistent with theory, with a noise-equivalent power of 7.5×10−18W/√Hz. The addition of Mn impurities did not significantly increase the heat capacity of the TES. In addition, the detector is surprisingly insensitive to applied magnetic fields. The use of AlMn alloy films in arrays of TES detectors has advantages in simplicity of fabrication when compared to traditional bilayer fabrication techniques.


Polarization Of Nuclear Spins From The Conductance Of Quantum Wires, James A. Nesteroff, Yuriy V. Pershin Dr, Vladimir Privman Sep 2004

Polarization Of Nuclear Spins From The Conductance Of Quantum Wires, James A. Nesteroff, Yuriy V. Pershin Dr, Vladimir Privman

Faculty Publications

We devise an approach to measure the polarization of nuclear spins via conductance measurements. Specifically, we study the combined effect of external magnetic field, nuclear spin polarization, and Rashba spin-orbit interaction on the conductance of a quantum wire. Nonequilibrium nuclear spin polarization affects the electron energy spectrum making it time dependent. Changes in the extremal points of the spectrum result in time dependence of the conductance. The conductance oscillation pattern can be used to obtain information about the amplitude of the nuclear spin polarization and extract the characteristic time scales of the nuclear spin subsystem.


Application Of Microgels For Optical Tagging, J. Michael Carthcart, L. Andrew Lyon, Marcus Weck, Robert D. Bock Sep 2004

Application Of Microgels For Optical Tagging, J. Michael Carthcart, L. Andrew Lyon, Marcus Weck, Robert D. Bock

Biology, Chemistry, and Environmental Sciences Faculty Books and Book Chapters

In this paper we present results from our research into the use of microgel-based photonic crystals in an optical tagging application. The basis for this research is the phenomena of self-assembly of hydrogel nano- and microparticles (i.e., microgels) into colloidal crystal Bragg reflectors. Previous research has demonstrated the assembly of Bragg structures that are sensitive in the visible spectral region. This current research focuses on the extension of this process into the infrared regime and the use of these infrared-sensitive structures in the creation of an optical tag. In particular, the research effort emphasizes two primary areas: the development of …


Oscillator Damped By A Constant-Magnitude Friction Force, Avi Marchewka, David S. Abbott, Robert J. Beichner Sep 2004

Oscillator Damped By A Constant-Magnitude Friction Force, Avi Marchewka, David S. Abbott, Robert J. Beichner

Dartmouth Scholarship

Although a simple spring/mass system damped by a friction force of constant magnitude shares many of the characteristics of the simple and damped harmonic oscillators, its solution is not presented in most texts. Closed form solutions for the turning and stopping points can be found using an energy-based approach. A dynamical approach leads to a closed form solution for the position of the mass as a function of time. The main result is that the amplitude of the oscillator damped by a constant magnitude friction force decreases by a constant amount each swing and the motion dies out after a …